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Bitruncated 16-cell honeycomb

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Bitruncated 16-cell honeycomb
(No image)
Type Uniform honeycomb
Schläfli symbol t1,2{3,3,4,3}
h2,3{4,3,3,4}
2t{3,31,1,1}
Coxeter-Dynkin diagram
=
=
4-face type Truncated 24-cell
Bitruncated tesseract
Cell type Cube
Truncated octahedron
Truncated tetrahedron
Face type {3}, {4}, {6}
Vertex figure
Coxeter group = [3,3,4,3]
= [4,3,31,1]
= [31,1,1,1]
Dual ?
Properties vertex-transitive

In four-dimensional Euclidean geometry, the bitruncated 16-cell honeycomb (or runcicantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.

Symmetry constructions

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There are 3 different symmetry constructions, all with 3-3 duopyramid vertex figures. The symmetry doubles on in three possible ways, while contains the highest symmetry.

Affine Coxeter group
[3,3,4,3]

[4,3,31,1]

[31,1,1,1]
Coxeter diagram
4-faces



See also

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Regular and uniform honeycombs in 4-space:

Notes

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References

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  • Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
  • Klitzing, Richard. "4D Euclidean tesselations". x3x3x *b3x *b3o, x3x3o *b3x4o, o3x3x4o3o - bithit - O107
Space Family / /
E2 Uniform tiling 0[3] δ3 3 3 Hexagonal
E3 Uniform convex honeycomb 0[4] δ4 4 4
E4 Uniform 4-honeycomb 0[5] δ5 5 5 24-cell honeycomb
E5 Uniform 5-honeycomb 0[6] δ6 6 6
E6 Uniform 6-honeycomb 0[7] δ7 7 7 222
E7 Uniform 7-honeycomb 0[8] δ8 8 8 133331
E8 Uniform 8-honeycomb 0[9] δ9 9 9 152251521
E9 Uniform 9-honeycomb 0[10] δ10 10 10
E10 Uniform 10-honeycomb 0[11] δ11 11 11
En-1 Uniform (n-1)-honeycomb 0[n] δn n n 1k22k1k21