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    http://en.wikipedia.org/wiki/Convex_uniform_honeycomb

    Panales Uniformes Convexos

    In geometry, a convex uniform honeycomb is a uniform space-filling tessellation in three-

    dimensional Euclidean spacewith non-overlapping convexuniform polyhedral cells.

    Twenty-eight such honeycombs exist:

    the familiarcubic honeycomb and 7 truncations thereof;

    the alternated cubic honeycomb and 4 truncations thereof;

    10 prismatic forms based on the uniform plane tilings (11 if including the cubic

    honeycomb);

    5 modifications of some of the above by elongation and/or gyration.

    They can be considered the three-dimensional analogue to the uniform tilings of the plane.

    Contents

    1 History

    o 1.1 Names

    2 Compact Euclidean uniform tessellations (by their infinite Coxeter group families)

    o 2.1 The C~3, [4,3,4] group (cubic)

    o 2.2 B~4, h[4,3,4], [4,31,1] group

    o 2.3 A~3 group

    o 2.4 Nonwythoffian forms (gyrated and elongated)

    o 2.5 Prismatic stacks

    2.5.1 The C~2xI~1(), [4,4] x [], prismatic group

    2.5.2 The H~2xI~1(), [6,3] x [] prismatic group

    o 2.6 Examples

    3 Noncompact forms

    4 Hyperbolic forms

    o 4.1 [3,5,3] family

    o 4.2 [5,3,4] family

    o 4.3 [5,3,5] family

    o 4.4 [5,31,1] family

    o 4.5 [4,3,3,3:] family

    o 4.6 [5,3,3,3:] family

    o 4.7 [4,3,4,3:] family

    o 4.8 [4,3,5,3:] family

    o 4.9 [5,3,5,3:] family

    5 Notes

    http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Tessellationhttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Uniform_polyhedronhttp://en.wikipedia.org/wiki/Uniform_polyhedronhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_R4.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Alternated_cubic_formshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Stacked_prismatic_formshttp://en.wikipedia.org/wiki/List_of_uniform_planar_tilingshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Historyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Nameshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Compact_Euclidean_uniform_tessellations_.28by_their_infinite_Coxeter_group_families.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E3.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E3.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E3.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E3.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E3.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#A.7E3_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#A.7E3_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#A.7E3_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#A.7E3_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#A.7E3_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Nonwythoffian_forms_.28gyrated_and_elongated.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Prismatic_stackshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Exampleshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Noncompact_formshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Hyperbolic_formshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B3.2C5.2C3.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C4.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C5.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C31.2C1.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C31.2C1.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C31.2C1.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B4.2C3.2C3.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C3.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B4.2C3.2C4.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B4.2C3.2C5.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C5.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Noteshttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Tessellationhttp://en.wikipedia.org/wiki/Euclidean_spacehttp://en.wikipedia.org/wiki/Uniform_polyhedronhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_R4.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Alternated_cubic_formshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Stacked_prismatic_formshttp://en.wikipedia.org/wiki/List_of_uniform_planar_tilingshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Historyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Nameshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Compact_Euclidean_uniform_tessellations_.28by_their_infinite_Coxeter_group_families.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E3.2C_.5B4.2C3.2C4.5D_group_.28cubic.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#B.7E4.2C_h.5B4.2C3.2C4.5D.2C_.5B4.2C31.2C1.5D_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#A.7E3_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Nonwythoffian_forms_.28gyrated_and_elongated.29http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Prismatic_stackshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_C.7E2xI.7E1.28.E2.88.9E.29.2C_.5B4.2C4.5D_x_.5B.E2.88.9E.5D.2C_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#The_H.7E2xI.7E1.28.E2.88.9E.29.2C_.5B6.2C3.5D_x_.5B.E2.88.9E.5D_prismatic_grouphttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Exampleshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Noncompact_formshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Hyperbolic_formshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B3.2C5.2C3.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C4.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C5.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C31.2C1.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B4.2C3.2C3.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C3.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B4.2C3.2C4.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B4.2C3.2C5.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#.5B5.2C3.2C5.2C3:.5D_familyhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Notes
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    6 References

    7 External links

    History

    1900:Thorold Gosset enumerated the list of semiregular convex polytopes withregular cells (Platonic solids) in his publication On the Regular and Semi-Regular

    Figures in Space of n Dimensions, including one regular cubic honeycomb, and two

    semiregular forms with tetrahedra and octahedra.

    1905:Alfredo Andreini enumerated 25 of these tessellations.

    1991:Norman Johnson's manuscript Uniform Polytopes identified the complete list

    of 28.

    1994:Branko Grnbaum, in his paperUniform tilings of 3-space, also

    independently enumerated all 28, after discovering errors in Andreini's publication.

    He found the 1905 paper, which listed 25, had 1 wrong, and 4 being missing.

    Grnbaum also states thatI. Alexeyev of Russia also independently enumeratedthese forms around the same time.

    2006:George Olshevsky, in his manuscript Uniform Panoploid Tetracombs, along

    with repeating the derived list of 11 convex uniform tilings, and 28 convex uniformhoneycombs, expands a further derived list of 143 convex uniform tetracombs

    (Honeycombs ofuniform polychorons in 4-space).

    Only 14 of the convex uniform polyhedra appear in these patterns:

    three of the five Platonic solids,

    six of the thirteenArchimedean solids, and

    five of the infinite family ofprisms.

    Names

    This set can be called the regular and semiregular honeycombs. It has been called the

    Archimedean honeycombs by analogy with the convex uniform (non-regular) polyhedra,

    commonly called Archimedean solids. Recently Conwayhas suggested naming the set as

    the Architectonic tessellations and the dual honeycombs as the Catoptric tessellations.

    The individual honeycombs are listed with names given to them byNorman Johnson.

    (Some of the terms used below are defined in Uniform polychoron#Geometric derivations.)

    For cross-referencing, they are given with list indices from [A]ndreini (1-22), [W]illiams(1-

    2,9-19), [J]ohnson (11-19, 21-25, 31-34, 41-49, 51-52, 61-65), and [G]runbaum(1-28).

    Compact Euclidean uniform tessellations (by their

    infinite Coxeter group families)

    http://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Referenceshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#External_linkshttp://en.wikipedia.org/wiki/Thorold_Gossethttp://en.wikipedia.org/wiki/Thorold_Gossethttp://en.wikipedia.org/wiki/Platonic_solidhttp://en.wikipedia.org/wiki/Alfredo_Andreinihttp://en.wikipedia.org/wiki/Alfredo_Andreinihttp://en.wikipedia.org/wiki/Norman_Johnson_(mathematician)http://en.wikipedia.org/wiki/Norman_Johnson_(mathematician)http://en.wikipedia.org/wiki/Branko_Gr%C3%BCnbaumhttp://en.wikipedia.org/wiki/Branko_Gr%C3%BCnbaumhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Gyrated_and_elongated_formshttp://en.wikipedia.org/w/index.php?title=I._Alexeyev&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=I._Alexeyev&action=edit&redlink=1http://en.wikipedia.org/wiki/George_Olshevskyhttp://en.wikipedia.org/wiki/George_Olshevskyhttp://en.wikipedia.org/wiki/Uniform_polychoronhttp://en.wikipedia.org/wiki/Uniform_polychoronhttp://en.wikipedia.org/wiki/Platonic_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Prism_(geometry)http://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/John_Horton_Conwayhttp://en.wikipedia.org/wiki/John_Horton_Conwayhttp://en.wikipedia.org/wiki/Norman_Johnsonhttp://en.wikipedia.org/wiki/Norman_Johnsonhttp://en.wikipedia.org/wiki/Uniform_polychoron#Geometric_derivationshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Referenceshttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#External_linkshttp://en.wikipedia.org/wiki/Thorold_Gossethttp://en.wikipedia.org/wiki/Platonic_solidhttp://en.wikipedia.org/wiki/Alfredo_Andreinihttp://en.wikipedia.org/wiki/Norman_Johnson_(mathematician)http://en.wikipedia.org/wiki/Branko_Gr%C3%BCnbaumhttp://en.wikipedia.org/wiki/Convex_uniform_honeycomb#Gyrated_and_elongated_formshttp://en.wikipedia.org/w/index.php?title=I._Alexeyev&action=edit&redlink=1http://en.wikipedia.org/wiki/George_Olshevskyhttp://en.wikipedia.org/wiki/Uniform_polychoronhttp://en.wikipedia.org/wiki/Platonic_solidhttp://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/Prism_(geometry)http://en.wikipedia.org/wiki/Archimedean_solidhttp://en.wikipedia.org/wiki/John_Horton_Conwayhttp://en.wikipedia.org/wiki/Norman_Johnsonhttp://en.wikipedia.org/wiki/Uniform_polychoron#Geometric_derivations
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    Fundamental domains in a cubic element of three groups.

    The fundamental infinite Coxeter groups for 3-space are:

    1. The C~3, [4,3,4], cubic, (8 unique forms plus one alternation)

    2. The B~3, [4,31,1], alternated cubic, (11 forms, 3 new)

    3. The A~3 cyclic group, (5 forms, one new)

    In addition there are 5 special honeycombs which don't have pure reflectional symmetryand are constructed from reflectional forms with elongation andgyration operations.

    The total unique honeycombs above are 18.

    The prismatic stacks from infinite Coxeter groups for 3-space are:

    1. The C~2xI~

    1, [4,4]x[] prismatic group, (2 new forms)

    2. The H~2xI~

    1, [6,3]x[] prismatic group, (7 unique forms)

    3. The A~2xI~

    1, []x[] prismatic group, (No new forms)

    4. The I~1xI~

    1xI~

    1, []x[]x[] prismatic group, (These all become a

    cubic honeycomb)

    In addition there is one special elongatedform of the triangular prismatic honeycomb.

    The total unique prismatic honeycombs above (excluding the cubic counted previously) are10.

    Combining these counts, 18 and 10 gives us the total 28 uniform honeycombs.

    The C~3, [4,3,4] group (cubic)

    http://en.wikipedia.org/wiki/Coxeter_grouphttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_infin.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_2.pnghttp://en.wikipedia.org/wiki/File:CD_righttriangle-000.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-33.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Coxeter-Dynkin_3-space_groups.pnghttp://en.wikipedia.org/wiki/Coxeter_group
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    The regular cubic honeycomb, represented by Schlfli symbol {4,3,4}, offers seven unique

    derived uniform honeycombs via truncation operations. (One redundant form, theruncinated cubic honeycomb, is included for completeness though identical to the cubichoneycomb.)

    Reference

    Indices

    Honeycomb

    name

    Coxeter-

    Dynkin

    and Schlfli

    symbols

    Cell counts/vertex

    and positions in cubic

    honeycomb

    (0)(1) (2)

    (3) Solids

    (Partial)

    Frames

    (Perspective)Vertex figure

    J11,15A1W1G22

    cubic

    t0{4,3,4}

    (8)

    (4.4.4)octahedron

    J12,32A15W14G7

    rectified cubic

    t1{4,3,4}

    (2)

    (3.3.3.3)

    (4)

    (3.4.3.4)cuboid

    J13A14W15G8

    truncated

    cubic

    t0,1{4,3,4}

    (1)

    (3.3.3.3)

    (4)

    (3.8.8) square

    pyramid

    J14A17W12G9

    cantellatedcubic

    t0,2{4,3,4}

    (1)

    (3.4.3.4)

    (2)

    (4.4.4)

    (2)

    (3.4.4.4)wedge

    J11,15

    runcinated

    cubic

    (same asregularcubic)

    t0,3{4,3,4}

    (1)

    (4.4.4)

    (3)

    (4.4.4)

    (3)

    (4.4.4)

    (1)

    (4.4.4)octahedron

    J16A3W2G28

    bitruncatedcubic

    t1,2{4,3,4}

    (2)

    (4.6.6)

    (2)

    (4.6.6)

    http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol#Extended_for_uniform_polychora_and_3-space_honeycombshttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Truncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Cantellated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantellated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Wedge_(geometry)http://en.wikipedia.org/wiki/Runcination_(geometry)http://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/File:Bitruncated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Bitruncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Bitruncated_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Truncated_octahedron.pnghttp://en.wikipedia.org/wiki/File:Truncated_octahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Runcinated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Runcinated_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Cantellated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cantellated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Cantellated_cubic_honeycomb.jpghttp://en.wikipedia.org/wiki/File:Small_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:Cuboctahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Truncated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Truncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Truncated_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Truncated_hexahedron.pnghttp://en.wikipedia.org/wiki/File:Octahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Cuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Octahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Partial_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_dash.pnghttp://en.wikipedia.org/wiki/File:CDW_2c.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2c.pnghttp://en.wikipedia.org/wiki/File:CDW_dash.pnghttp://en.wikipedia.org/wiki/File:CDW_2c.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2c.pnghttp://en.wikipedia.org/wiki/File:CDW_dash.pnghttp://en.wikipedia.org/wiki/File:CDW_2c.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2c.pnghttp://en.wikipedia.org/wiki/File:CDW_dash.pnghttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol#Extended_for_uniform_polychora_and_3-space_honeycombshttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Truncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Cantellated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantellated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Wedge_(geometry)http://en.wikipedia.org/wiki/Runcination_(geometry)http://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedron
  • 8/9/2019 PANALES CONVEXOS

    5/26

    (disphenoid

    tetrahedron)

    J17A18

    W13G25

    cantitruncatedcubic

    t0,1,2{4,3,4}

    (1)

    (4.6.6)

    (1)

    (4.4.4)

    (2)

    (4.6.8) irregulartetrahedron

    J18A19W19G20

    runcitruncatedcubic

    t0,1,3{4,3,4}

    (1)

    (3.4.4.4)

    (1)

    (4.4.4)

    (2)

    (4.4.8)

    (1)

    (3.8.8)oblique

    trapezoidalpyramid

    J19A22W18G27

    omnitruncated

    cubic

    t0,1,2,3{4,3,4}

    (1)

    (4.6.8)

    (1)

    (4.4.8)

    (1)

    (4.4.8)

    (1)

    (4.6.8) irregular

    tetrahedron

    J21,31,51A2W9G1

    alternated

    cubic

    h0{4,3,4}

    (6)

    (3.3.3.3)

    (8)

    (3.3.3)cuboctahedron

    B~

    4, h[4,3,4], [4,31,1

    ] group

    The B~4 group offers 11 derived forms via truncation operations, four being unique uniformhoneycombs.

    The honeycombs from this group are called alternated cubic because the first form can be

    seen as a cubic honeycomb with alternate vertices removed, reducing cubic cells to

    tetrahedra and creating octahedron cells in the gaps.

    Nodes are indexed left to right as 0,1,0',3 with 0' being below and interchangeable with 0.

    The alternate cubic names given are based on this ordering.

    Referenced

    indices

    Honeycomb

    name

    Coxeter-

    Dynkin

    diagram

    Cells by location

    (and count around each vertex)Solids

    (Partial)

    Frames

    (Perspective)verte(0) (1) (0') (3)

    http://en.wikipedia.org/wiki/Disphenoid_tetrahedronhttp://en.wikipedia.org/wiki/Disphenoid_tetrahedronhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Runcitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Runcitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octagonal_prismhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Omnitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Omnitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Octagonal_prismhttp://en.wikipedia.org/wiki/Octagonal_prismhttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/File:CD_dash.pnghttp://en.wikipedia.org/wiki/File:CD_2c.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-0dash.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_2.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-dash0.pnghttp://en.wikipedia.org/wiki/File:CD_2c.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_2c.pnghttp://en.wikipedia.org/wiki/File:CD_dash.pnghttp://en.wikipedia.org/wiki/File:Alternated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Tetrahedral-octahedral_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Octahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_hole.pnghttp://en.wikipedia.org/wiki/File:Omnitruncated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Omnitruncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Omnitruncated_cubic_honeycomb.jpghttp://en.wikipedia.org/wiki/File:Great_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Octagonal_prism.pnghttp://en.wikipedia.org/wiki/File:Octagonal_prism.pnghttp://en.wikipedia.org/wiki/File:Great_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Runcitruncated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Runcitruncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Runcitruncated_cubic_honeycomb.jpghttp://en.wikipedia.org/wiki/File:Truncated_hexahedron.pnghttp://en.wikipedia.org/wiki/File:Octagonal_prism.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:Small_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_Cubic_Honeycomb.svghttp://en.wikipedia.org/wiki/File:Great_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:Truncated_octahedron.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/Disphenoid_tetrahedronhttp://en.wikipedia.org/wiki/Disphenoid_tetrahedronhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Runcitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Runcitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octagonal_prismhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Omnitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Omnitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Octagonal_prismhttp://en.wikipedia.org/wiki/Octagonal_prismhttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Vertex_figure
  • 8/9/2019 PANALES CONVEXOS

    6/26

    J21,31,51A2W9G1

    alternated cubic (6)

    (3.3.3.3)(8)

    (3.3.3)

    cuboc

    J22,34A21W17G10

    truncatedalternated cubic (1)

    (3.4.3.4) (2)

    (4.6.6)(2)

    (3.6.6)

    J12,32A15W14G7

    rectified cubic

    (rectifiedalternate cubic) (2)

    (3.4.3.4) (2)

    (3.4.3.4)

    (2)

    (3.3.3.3)

    cu

    J12,32

    A15W14G7

    rectified cubic(cantellated

    alternate cubic) (1)(3.3.3.3)

    (1)(3.3.3.3)

    (4)(3.4.3.4)

    cu

    J16A3W2G28

    bitruncatedcubic

    (cantitruncated

    alternate cubic)(1)

    (4.6.6) (1)

    (4.6.6)(2)

    (4.6.6)iso

    tetra

    J13

    A14W15G8

    truncated cubic

    (bicantellatedalternate cubic) (2)

    (3.8.8) (2)

    (3.8.8)

    (1)

    (3.3.3.3)sq

    pyr

    J11,15A1W1G22

    cubic

    (trirectified

    alternate cubic) (4)(4.4.4)

    (4)(4.4.4)

    octa

    J23A16W11G5

    runcinated

    alternated cubic (1)cube

    (3)(3.4.4.4)

    (1)(3.3.3)

    J14A17W12G9

    cantellated cubic(runcicantellated

    alternate cubic) (1)

    (3.4.4.4)

    (2

    )

    (4.4.4)

    (1)

    (3.4.4.4)

    (1)

    (3.4.3.4)

    w

    http://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Truncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Runcinated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Runcinated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Rhombicuboctahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cantellated_cubic_honeycombhttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Wedge_(geometry)http://en.wikipedia.org/wiki/File:Runcicantellated_alternate_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cantellated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Cantellated_cubic_honeycomb.jpghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t02.pnghttp://en.wikipedia.org/wiki/File:Small_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron_222-t012.pnghttp://en.wikipedia.org/wiki/File:Small_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-01.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:Runcinated_alternated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Runcinated_alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Runcinated_alternated_cubic_honeycomb.jpghttp://en.wikipedia.org/wiki/File:Tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Small_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:Cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Bicolor_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:Hexahedron.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:Bicantellated_alternate_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Truncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Truncated_cubic_honeycomb2.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t1.pnghttp://en.wikipedia.org/wiki/File:Truncated_hexahedron.pnghttp://en.wikipedia.org/wiki/File:Truncated_hexahedron.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_alternate_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Bitruncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Bitruncated_cubic_honeycomb3.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t012.pnghttp://en.wikipedia.org/wiki/File:Truncated_octahedron.pnghttp://en.wikipedia.org/wiki/File:Truncated_octahedron.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-11.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:Cantellated_alternate_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_honeycomb3.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t02.pnghttp://en.wikipedia.org/wiki/File:Octahedron.pnghttp://en.wikipedia.org/wiki/File:Octahedron.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-01.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:Rectified_alternate_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_honeycomb4.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t1.pnghttp://en.wikipedia.org/wiki/File:Cuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Cuboctahedron.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:Truncated_alternated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Truncated_alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Truncated_Alternated_Cubic_Honeycomb.svghttp://en.wikipedia.org/wiki/File:Truncated_tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Truncated_octahedron.pnghttp://en.wikipedia.org/wiki/File:Cuboctahedron.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:Alternated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Tetrahedral-octahedral_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Octahedron.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Truncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Square_pyramidhttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Runcinated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Runcinated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Rhombicuboctahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cantellated_cubic_honeycombhttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Small_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Wedge_(geometry)
  • 8/9/2019 PANALES CONVEXOS

    7/26

    J24A20W16G21

    cantitruncated

    alternated cubic

    (orruncitruncated

    alternate cubic)

    (1)

    (3.8.8) (2)

    (4.6.8)

    (1)

    (3.6.6)

    J17A18W13G25

    cantitruncated

    cubic

    (omnitruncated

    alternated cubic)(1)

    (4.6.8)

    (1)(4.4.4)

    (1)(4.6.8)

    (1)(4.6.6)

    irretetra

    [edit] A~3 group

    There are 5 forms constructed from the A

    ~

    3 group, only the quarter cubic honeycomb isunique.

    Referenced

    indices

    Honeycomb

    name

    Coxeter-

    Dynkin

    diagram

    Cells by location

    (and count around each vertex)Solids

    (Partial)

    Frames

    (Perspective)vertex figu(0) (1) (2) (3)

    J21,31,51A2W9

    G1

    alternated

    cubic (4)

    (3.3.3)

    (6)

    (3.3.3.3)

    (4)

    (3.3.3)cuboctahedr

    J12,32A15W14G7

    rectified

    cubic (2)(3.4.3.4)

    (1)(3.3.3.3)

    (2)(3.4.3.4)

    (1)(3.3.3.3)

    cuboid

    J25,33A13

    W10

    G6

    quartercubic (1)

    (3.3.3)

    (1)

    (3.3.3)

    (3)

    (3.6.6)

    (3)

    (3.6.6) Elongatedtriangularantiprism

    J22,34A21W17G10

    truncated

    alternated

    cubic

    (1)

    (3.6.6)

    (1)

    (3.4.3.4)

    (1)

    (3.6.6)

    (2)

    (4.6.6)

    Rectangula

    http://en.wikipedia.org/wiki/Cantitruncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantitruncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Truncated_cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=6http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Quarter_cubic_honeycombhttp://en.wikipedia.org/wiki/Quarter_cubic_honeycombhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/File:T012_quarter_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Truncated_alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Truncated_Alternated_Cubic_Honeycomb.svghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t012.pnghttp://en.wikipedia.org/wiki/File:Truncated_tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t02.pnghttp://en.wikipedia.org/wiki/File:Truncated_tetrahedron.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10-right-3.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-33b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-11-left-3.pnghttp://en.wikipedia.org/wiki/File:T01_quarter_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Bitruncated_alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Quarter_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Truncated_tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Truncated_tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Tetrahedron.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10-right-3.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-33b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10-left-3.pnghttp://en.wikipedia.org/wiki/File:T02_quarter_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Rectified_cubic_honeycomb2.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t1.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t02.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t1.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t02.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-01-right-3.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-33b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10-left-3.pnghttp://en.wikipedia.org/wiki/File:Alternated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Tetrahedral-octahedral_honeycomb2.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t2.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t1.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t0.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-33b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10-left-3.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_3.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-0dash.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-0dash.pnghttp://en.wikipedia.org/wiki/File:CD_3.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-dash0.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-23.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-00.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-23.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-dash0.pnghttp://en.wikipedia.org/wiki/File:Omnitruncated_alternated_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_Cubic_Honeycomb.svghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t012.pnghttp://en.wikipedia.org/wiki/File:Great_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron_222-t012.pnghttp://en.wikipedia.org/wiki/File:Great_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-11.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:Runcitruncated_alternate_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Cantitruncated_alternated_cubic_honeycomb.jpghttp://en.wikipedia.org/wiki/File:Truncated_tetrahedron.pnghttp://en.wikipedia.org/wiki/File:Great_rhombicuboctahedron.pnghttp://en.wikipedia.org/wiki/File:Truncated_hexahedron.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/File:CD_4.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-10.pnghttp://en.wikipedia.org/wiki/File:CD_3b.pnghttp://en.wikipedia.org/wiki/File:CD_ring.pnghttp://en.wikipedia.org/wiki/Cantitruncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantitruncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_cubehttp://en.wikipedia.org/wiki/Truncated_cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Cantitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/wiki/Great_rhombicuboctahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=6http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Rectified_cubic_honeycombhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Cuboidhttp://en.wikipedia.org/wiki/Quarter_cubic_honeycombhttp://en.wikipedia.org/wiki/Quarter_cubic_honeycombhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Cuboctahedronhttp://en.wikipedia.org/wiki/Truncated_tetrahedronhttp://en.wikipedia.org/wiki/Truncated_octahedron
  • 8/9/2019 PANALES CONVEXOS

    8/26

    pyramid

    J16A3W2

    G28

    bitruncatedcubic (1)

    (4.6.6)

    (1)

    (4.6.6)

    (1)

    (4.6.6)

    (1)

    (4.6.6)

    isoscelestetrahedron

    Nonwythoffian forms (gyrated and elongated)

    Three more uniform honeycombs are generated by breaking one or another of the abovehoneycombs where its faces form a continuous plane, then rotating alternate layers by 60 or

    90 degrees (gyration) and/or inserting a layer of prisms (elongation).

    The elongated and gyroelongated alternated cubic tilings have the same vertex figure, but

    are not alike. In the elongatedform, each prism meets a tetrahedron at one triangular end

    and an octahedron at the other. In thegyroelongatedform, prisms that meet tetrahedra atboth ends alternate with prisms that meet octahedra at both ends.

    The gyroelongated triangular prismatic tiling has the same vertex figure as one of the plain

    prismatic tilings; the two may be derived from the gyrated and plain triangular prismatictilings, respectively, by inserting layers of cubes.

    Referenced

    indicessymbol

    Honeycomb

    name

    cell types

    (# at each

    vertex)

    Solids

    (Partial)

    Frames

    (Perspective)vertex figure

    J52A2'G2

    h{4,3,4}:ggyrated

    alternated

    cubic

    tetrahedron(8)

    octahedron

    (6) triangular

    orthobicupola

    J61A?G3

    h{4,3,4}:ge

    gyroelongated

    alternated

    cubic

    triangular

    prism (6)tetrahedron

    (4)

    octahedron(3)

    -

    J62A?G4

    h{4,3,4}:eelongatedalternated

    cubic

    triangular

    prism (6)tetrahedron

    (4)

    octahedron

    (3)

    http://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Gyrated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Triangular_orthobicupolahttp://en.wikipedia.org/wiki/Triangular_orthobicupolahttp://en.wikipedia.org/wiki/Gyroelongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Elongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Elongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Elongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/File:Elongated_alternated_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/File:VF-extended_alternated_cubic.pnghttp://en.wikipedia.org/wiki/File:Elongated_alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Elongated_alternated_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Gyroelongated_alternated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Gyroelongated_alternated_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:VF-gyrated_alternated_cubic.pnghttp://en.wikipedia.org/wiki/File:Gyrated_alternated_cubic.pnghttp://en.wikipedia.org/wiki/File:Gyrated_alternated_cubic.jpghttp://en.wikipedia.org/wiki/File:T0123_quarter_cubic_honeycomb_verf.pnghttp://en.wikipedia.org/wiki/File:Bitruncated_cubic_tiling.pnghttp://en.wikipedia.org/wiki/File:Bitruncated_cubic_honeycomb2.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t012.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t012.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t012.pnghttp://en.wikipedia.org/wiki/File:Uniform_polyhedron-33-t012.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-11-right-3.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-33b.pnghttp://en.wikipedia.org/wiki/File:CD_downbranch-11-left-3.pnghttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Bitruncated_cubic_honeycombhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Truncated_octahedronhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Gyrated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Triangular_orthobicupolahttp://en.wikipedia.org/wiki/Triangular_orthobicupolahttp://en.wikipedia.org/wiki/Gyroelongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Octahedronhttp://en.wikipedia.org/wiki/Elongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Elongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Elongated_alternated_cubic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Tetrahedronhttp://en.wikipedia.org/wiki/Octahedron
  • 8/9/2019 PANALES CONVEXOS

    9/26

    J63A?G12

    {3,6}:g x{}

    gyrated

    triangularprismatic

    triangularprism (12)

    J64A?G15

    {3,6}:ge x{}

    gyroelongatedtriangularprismatic

    triangularprism (6)cube (4)

    [edit] Prismatic stacks

    Eleven prismatic tilings are obtained by stacking the eleven uniform plane tilings, shown

    below, in parallel layers. (One of these honeycombs is the cubic, shown above.) The vertexfigure of each is an irregularbipyramid whose faces areisosceles triangles.

    [edit] The C

    ~

    2xI

    ~

    1(), [4,4] x [], prismatic group

    There's only 3 unique honeycombs from the square tiling, but all 6 tiling truncations are

    listed below for completeness, and tiling images are shown by colors corresponding to eachform.

    Indices

    Coxeter-

    Dynkin

    and Schlfli

    symbols

    Honeycomb namePlane

    tiling

    Solids

    (Partial)Tiling

    J11,15A1G22

    {4,4} x {}Cubic

    (Square prismatic)(4.4.4.4)

    J45A6G24

    t0,1{4,4} x

    {}

    Truncated/Bitruncated square

    prismatic(4.8.8)

    J11,15A1G22

    t1{4,4} x {}

    Cubic

    (Rectified square prismatic)(4.4.4.4)

    J11,15A1G22

    t0,2{4,4} x

    {}

    Cubic

    (Cantellated square prismatic)(4.4.4.4)

    http://en.wikipedia.org/wiki/Gyrated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Gyroelongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=8http://en.wikipedia.org/wiki/Tiling_by_regular_polygonshttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Bipyramidhttp://en.wikipedia.org/wiki/Isosceles_trianglehttp://en.wikipedia.org/wiki/Isosceles_trianglehttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=9http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol#Extended_for_uniform_polychora_and_3-space_honeycombshttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Square_tilinghttp://en.wikipedia.org/wiki/Truncated_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_square_tilinghttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Square_tilinghttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Square_tilinghttp://en.wikipedia.org/wiki/File:Uniform_tiling_44-t02.pnghttp://en.wikipedia.org/wiki/File:Partial_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_44-t1.pnghttp://en.wikipedia.org/wiki/File:Square_prismatic_2-color_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_44-t01.pnghttp://en.wikipedia.org/wiki/File:Truncated_square_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_44-t0.pnghttp://en.wikipedia.org/wiki/File:Partial_cubic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:VF-prismatic_extended_triangular.pnghttp://en.wikipedia.org/wiki/File:Gyroelongated_triangular_prismatic_tiling.pnghttp://en.wikipedia.org/wiki/File:Gyroelongated_triangular_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:VF-gyrated_prismatic_triangular.pnghttp://en.wikipedia.org/wiki/File:Gyrated_triangular_prismatic_tiling.pnghttp://en.wikipedia.org/wiki/File:Gyrated_triangular_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/Gyrated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyrated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Gyroelongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Gyroelongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Triangular_prismhttp://en.wikipedia.org/wiki/Cubehttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=8http://en.wikipedia.org/wiki/Tiling_by_regular_polygonshttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Vertex_figurehttp://en.wikipedia.org/wiki/Bipyramidhttp://en.wikipedia.org/wiki/Isosceles_trianglehttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=9http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol#Extended_for_uniform_polychora_and_3-space_honeycombshttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Square_tilinghttp://en.wikipedia.org/wiki/Truncated_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_square_tilinghttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Square_tilinghttp://en.wikipedia.org/wiki/Cubic_honeycombhttp://en.wikipedia.org/wiki/Square_tiling
  • 8/9/2019 PANALES CONVEXOS

    10/26

    J45A6G24

    t0,1,2{4,4} x

    {}

    Truncated square prismatic

    (Omnitruncated squareprismatic)

    (4.8.8)

    J44A11G14 s{4,4} x {}

    Snub square prismatic (3.3.4.3.4)

    [edit] The H~2xI~1(), [6,3] x [] prismatic group

    Indices

    Coxeter-

    Dynkin

    and Schlfli

    symbols

    Honeycomb namePlane

    tiling

    Solids

    (Partial)Tiling

    J42A5G26

    t0{6,3} x {}Hexagonal prismatic (63)

    J46A7G19

    t0,1{6,3} x {}Truncated hexagonal prismatic (3.12.12)

    J43A8

    G18 t1{6,3} x {}

    Trihexagonal prismatic (3.6.3.6)

    J42A5G26

    t1,2{6,3} x {}

    Truncated triangular

    prismatic

    Hexagonal prismatic

    (6.6.6)

    J41A4G11

    t2{6,3} x {}Triangular prismatic (36)

    J47A9G16

    t0,2{6,3} x {}

    Rhombi-trihexagonal

    prismatic(3.4.6.4)

    http://en.wikipedia.org/wiki/Truncated_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_square_tilinghttp://en.wikipedia.org/wiki/Snub_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Snub_square_tilinghttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=10http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol#Extended_for_uniform_polychora_and_3-space_honeycombshttp://en.wikipedia.org/wiki/Hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Hexagonal_tilinghttp://en.wikipedia.org/wiki/Hexagonal_tilinghttp://en.wikipedia.org/wiki/Hexagonal_tilinghttp://en.wikipedia.org/wiki/Hexagonal_tilinghttp://en.wikipedia.org/wiki/Truncated_hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_hexagonal_tilinghttp://en.wikipedia.org/wiki/Triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Trihexagonal_tilinghttp://en.wikipedia.org/wiki/Hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Hexagonal_tilinghttp://en.wikipedia.org/wiki/Triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Triangular_tilinghttp://en.wikipedia.org/wiki/Triangular_tilinghttp://en.wikipedia.org/wiki/Triangular_tilinghttp://en.wikipedia.org/wiki/Triangular_tilinghttp://en.wikipedia.org/wiki/Rhombitriangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Rhombitriangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Small_rhombitrihexagonal_tilinghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-t02.pnghttp://en.wikipedia.org/wiki/File:Rhombitriangular-hexagonal_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-t2.pnghttp://en.wikipedia.org/wiki/File:Triangular_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-t12.pnghttp://en.wikipedia.org/wiki/File:Truncated_triangular_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-t1.pnghttp://en.wikipedia.org/wiki/File:Triangular-hexagonal_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-t01.pnghttp://en.wikipedia.org/wiki/File:Truncated_hexagonal_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-t0.pnghttp://en.wikipedia.org/wiki/File:Hexagonal_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_44-snub.pnghttp://en.wikipedia.org/wiki/File:Snub_square_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_hole.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_hole.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_hole.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_44-t012.pnghttp://en.wikipedia.org/wiki/File:Truncated_square_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/Truncated_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_square_tilinghttp://en.wikipedia.org/wiki/Snub_square_prismatic_honeycombhttp://en.wikipedia.org/wiki/Snub_square_tilinghttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=10http://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol#Extended_for_uniform_polychora_and_3-space_honeycombshttp://en.wikipedia.org/wiki/Hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Hexagonal_tilinghttp://en.wikipedia.org/wiki/Truncated_hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Truncated_hexagonal_tilinghttp://en.wikipedia.org/wiki/Triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Trihexagonal_tilinghttp://en.wikipedia.org/wiki/Hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Hexagonal_tilinghttp://en.wikipedia.org/wiki/Triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Triangular_tilinghttp://en.wikipedia.org/wiki/Rhombitriangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Rhombitriangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Small_rhombitrihexagonal_tiling
  • 8/9/2019 PANALES CONVEXOS

    11/26

    J49A10G23

    t0,1,2{6,3} x

    {}

    Omnitruncated trihexagonalprismatic

    (4.6.12)

    J48A12G17

    s{6,3} x {}Snub trihexagonal prismatic (3.3.3.3.6)

    J65A11'G13

    {3,6}:e x {} elongated triangular prismatic (3.3.3.4.4)

    [edit] Examples

    All 28 of these tessellations are found in crystal arrangements.[citation needed]

    The alternated cubic honeycomb is of special importance since its vertices form a cubic

    close-packing of spheres. The space-filling truss of packed octahedra and tetrahedra was

    apparently first discovered by Alexander Graham Bell and independently re-discovered byBuckminster Fuller(who called it the octet truss and patented it in the 1940s). [2][3][4]

    [5]. Octet trusses are now among the most common types of truss used in construction.

    [edit] Noncompact forms

    Ifcells are allowed to beuniform tilings, more uniform honeycombs can be defined:

    Families:

    C~2xA1: [4,4]x[ ] Cubic prismatic slab honeycomb (3 forms)

    H~2xA1: [6,3]x[ ] Tri-hexagonal prismatic slab honeycomb (8 forms)

    A~2xA1: []x[ ] triangular prismatic slab(No new forms)

    I~1xA1xA1: []x[ ]x[ ] = Cubic column honeycomb (1 form)

    I2(p)xI~

    1: [p]x[] Prismatic column honeycomb

    I

    ~

    1xI

    ~

    1xA1: []x[]x[ ] = [4,4]x[ ] - = (Same as cubic slabhoneycomb family)

    http://en.wikipedia.org/wiki/Omnitruncated_triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Omnitruncated_triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Great_rhombitrihexagonal_tilinghttp://en.wikipedia.org/wiki/Snub_triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Snub_hexagonal_tilinghttp://en.wikipedia.org/wiki/Elongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Elongated_triangular_tilinghttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=11http://en.wikipedia.org/wiki/Crystalhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Close-packinghttp://en.wikipedia.org/wiki/Trusshttp://en.wikipedia.org/wiki/Alexander_Graham_Bellhttp://en.wikipedia.org/wiki/Buckminster_Fullerhttp://en.wikipedia.org/wiki/Octet_trusshttp://tabletoptelephone.com/~hopspage/Fuller.htmlhttp://members.cruzio.com/~devarco/energy.htmhttp://www.n55.dk/MANUALS/DISCUSSIONS/OTHER_TEXTS/CM_TEXT.htmlhttp://www.cjfearnley.com/fuller-faq-2.htmlhttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=12http://en.wikipedia.org/wiki/Cell_(mathematics)http://en.wikipedia.org/wiki/Uniform_tilinghttp://en.wikipedia.org/wiki/Uniform_tilinghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/w/index.php?title=Cubic_prismatic_slab_honeycomb&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Tri-hexagonal_prismatic_slab_honeycomb&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Triangular_prismatic_slab&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Triangular_prismatic_slab&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Cubic_column_honeycomb&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Prismatic_column_honeycomb&action=edit&redlink=1http://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_p.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CD_dot.pnghttp://en.wikipedia.org/wiki/File:CD_2.pnghttp://en.wikipedia.org/wiki/File:CD_righttriangle-000.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_4.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:Tile_33344.svghttp://en.wikipedia.org/wiki/File:Elongated_triangular_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-snub.pnghttp://en.wikipedia.org/wiki/File:Snub_triangular-hexagonal_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_hole.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_hole.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_hole.pnghttp://en.wikipedia.org/wiki/File:Uniform_tiling_63-t012.pnghttp://en.wikipedia.org/wiki/File:Omnitruncated_triangular-hexagonal_prismatic_honeycomb.pnghttp://en.wikipedia.org/wiki/File:CDW_dot.pnghttp://en.wikipedia.org/wiki/File:CDW_infin.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_2.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_3.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/File:CDW_6.pnghttp://en.wikipedia.org/wiki/File:CDW_ring.pnghttp://en.wikipedia.org/wiki/Omnitruncated_triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Omnitruncated_triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Great_rhombitrihexagonal_tilinghttp://en.wikipedia.org/wiki/Snub_triangular-hexagonal_prismatic_honeycombhttp://en.wikipedia.org/wiki/Snub_hexagonal_tilinghttp://en.wikipedia.org/wiki/Elongated_triangular_prismatic_honeycombhttp://en.wikipedia.org/wiki/Elongated_triangular_tilinghttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=11http://en.wikipedia.org/wiki/Crystalhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycombhttp://en.wikipedia.org/wiki/Close-packinghttp://en.wikipedia.org/wiki/Trusshttp://en.wikipedia.org/wiki/Alexander_Graham_Bellhttp://en.wikipedia.org/wiki/Buckminster_Fullerhttp://en.wikipedia.org/wiki/Octet_trusshttp://tabletoptelephone.com/~hopspage/Fuller.htmlhttp://members.cruzio.com/~devarco/energy.htmhttp://www.n55.dk/MANUALS/DISCUSSIONS/OTHER_TEXTS/CM_TEXT.htmlhttp://www.cjfearnley.com/fuller-faq-2.htmlhttp://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=12http://en.wikipedia.org/wiki/Cell_(mathematics)http://en.wikipedia.org/wiki/Uniform_tilinghttp://en.wikipedia.org/w/index.php?title=Cubic_prismatic_slab_honeycomb&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Tri-hexagonal_prismatic_slab_honeycomb&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Triangular_prismatic_slab&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Cubic_column_honeycomb&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Prismatic_column_honeycomb&action=edit&redlink=1
  • 8/9/2019 PANALES CONVEXOS

    12/26

    Examples (partially drawn): Cubic slab honeycomb and Alternated hexagonal slabhoneycomb.

    [edit] Hyperbolic forms

    There are 9 Coxeter group families of compact uniform honeycombs in hyperbolic 3-space,

    generated as Wythoff constructions, and represented by ring permutations of theCoxeter-Dynkin diagrams for each family.

    From these 9 families, there are a total of 76 unique honeycombs generated:

    1. [3,5,3] :

    2. [5,3,4] :

    3. [5,3,5] :

    4. [5,31,1] :

    5. [4,3,3,3:] :

    6. [4,3,4,3:] :

    7. [5,3,3,3:] :

    8. [5,3,4,3:] :

    9. [5,3,5,3:] :

    The full list of hyperbolic uniform honeycombs has not been proven and an unknown

    number of non-wythoffian exist. One known example is given with the {3,5,3} family

    below.

    [edit] [3,5,3] family

    There are 9 forms, generated by ring permutations of the Coxeter group: [3,5,3] or

    One related non-wythoffian form is constructed from the {3,5,3} vertex figure with 4

    (tetrahedrally arranged) vertices removed, creating pentagonal antiprisms and dodecahedra

    filling in the gaps.[1]

    # Honeycomb Cell counts/vertex

    http://en.wikipedia.org/w/index.php?title=Convex_uniform_honeycomb&action=edit&section=13http://en.wikipedia.org/wiki/Coxeter_grouphttp://en.wikipedia.org/wiki/Hyperbolic_spacehttp://en.wikipedia.org/wiki/Wythoff_constructionhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/Coxeter-Dynkin_diagramhttp://en.wikipedia.org/wiki/