Bitruncated 16-cell honeycomb

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.

Bitruncated 16-cell honeycomb
(No image)
TypeUniform honeycomb
Schläfli symbolt1,2{3,3,4,3}
h2,3{4,3,3,4}
2t{3,31,1,1}
Coxeter-Dynkin diagram
=
=
4-face typeTruncated 24-cell
Bitruncated tesseract
Cell typeCube
Truncated octahedron
Truncated tetrahedron
Face type{3}, {4}, {6}
Vertex figuretriangular duopyramid
Coxeter group = [3,3,4,3]
= [4,3,31,1]
= [31,1,1,1]
Dual?
Propertiesvertex-transitive

Symmetry constructions

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

Regular and uniform honeycombs in 4-space:

Notes

    References

    • 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
      • (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 {3[3]} δ3 hδ3 qδ3 Hexagonal
    E3 Uniform convex honeycomb {3[4]} δ4 hδ4 qδ4
    E4 Uniform 4-honeycomb {3[5]} δ5 hδ5 qδ5 24-cell honeycomb
    E5 Uniform 5-honeycomb {3[6]} δ6 hδ6 qδ6
    E6 Uniform 6-honeycomb {3[7]} δ7 hδ7 qδ7 222
    E7 Uniform 7-honeycomb {3[8]} δ8 hδ8 qδ8 133331
    E8 Uniform 8-honeycomb {3[9]} δ9 hδ9 qδ9 152251521
    E9 Uniform 9-honeycomb {3[10]} δ10 hδ10 qδ10
    En-1 Uniform (n-1)-honeycomb {3[n]} δn hδn qδn 1k22k1k21
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