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(Top)
 


1 Related honeycombs  



1.1  Quadritruncated 7-cubic honeycomb  







2 See also  





3 References  














7-cubic honeycomb






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From Wikipedia, the free encyclopedia
 

(Redirected from 7-cube honeycomb)

7-cubic honeycomb
(no image)
Type Regular 7-honeycomb
Uniform 7-honeycomb
Family Hypercube honeycomb
Schläfli symbol {4,35,4}
{4,34,31,1}
{∞}(7)
Coxeter-Dynkin diagrams

7-face type {4,3,3,3,3,3}
6-face type {4,3,3,3,3}
5-face type {4,3,3,3}
4-face type {4,3,3}
Cell type {4,3}
Face type {4}
Face figure {4,3}
(octahedron)
Edge figure 8{4,3,3}
(16-cell)
Vertex figure 128 {4,35}
(7-orthoplex)
Coxeter group [4,35,4]
Dual self-dual
Properties vertex-transitive, edge-transitive, face-transitive, cell-transitive

The 7-cubic honeycomborhepteractic honeycomb is the only regular space-filling tessellation (orhoneycomb) in Euclidean 7-space.

It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space.

There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol {4,35,4}. Another form has two alternating 7-cube facets (like a checkerboard) with Schläfli symbol {4,34,31,1}. The lowest symmetry Wythoff construction has 128 types of facets around each vertex and a prismatic product Schläfli symbol {∞}(7).

Related honeycombs[edit]

The [4,35,4], , Coxeter group generates 255 permutations of uniform tessellations, 135 with unique symmetry and 134 with unique geometry. The expanded 7-cubic honeycomb is geometrically identical to the 7-cubic honeycomb.

The 7-cubic honeycomb can be alternated into the 7-demicubic honeycomb, replacing the 7-cubes with 7-demicubes, and the alternated gaps are filled by 7-orthoplex facets.

Quadritruncated 7-cubic honeycomb[edit]

Aquadritruncated 7-cubic honeycomb, , contains all tritruncated 7-orthoplex facets and is the Voronoi tessellation of the D7* lattice. Facets can be identically colored from a doubled ×2, [[4,35,4]] symmetry, alternately colored from , [4,35,4] symmetry, three colors from , [4,34,31,1] symmetry, and 4 colors from , [31,1,33,31,1] symmetry.

See also[edit]

References[edit]

  • t
  • e
  • Space Family / /
    E2 Uniform tiling {3[3]} δ3 3 3 Hexagonal
    E3 Uniform convex honeycomb {3[4]} δ4 4 4
    E4 Uniform 4-honeycomb {3[5]} δ5 5 5 24-cell honeycomb
    E5 Uniform 5-honeycomb {3[6]} δ6 6 6
    E6 Uniform 6-honeycomb {3[7]} δ7 7 7 222
    E7 Uniform 7-honeycomb {3[8]} δ8 8 8 133331
    E8 Uniform 8-honeycomb {3[9]} δ9 9 9 152251521
    E9 Uniform 9-honeycomb {3[10]} δ10 10 10
    E10 Uniform 10-honeycomb {3[11]} δ11 11 11
    En-1 Uniform (n-1)-honeycomb {3[n]} δn n n 1k22k1k21

    Retrieved from "https://en.wikipedia.org/w/index.php?title=7-cubic_honeycomb&oldid=1157439972"

    Categories: 
    Honeycombs (geometry)
    8-polytopes
    Regular tessellations
     



    This page was last edited on 28 May 2023, at 16:32 (UTC).

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