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Stericantitruncated tesseractic honeycomb

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Stericantitruncated tesseractic honeycomb
(No image)
Type Uniform honeycomb
Schläfli symbol t0,1,2,4{4,3,3,4}
Coxeter-Dynkin diagrams
4-face type

runcitruncated 16-cell
cantitruncated tesseract
rhombicuboctahedral prism
truncated cuboctahedral prism
4-8 duoprism

Cell type Truncated cuboctahedron
Rhombicuboctahedron
Truncated tetrahedron
Octagonal prism
Hexagonal prism
Cube
Triangular prism
Face type {3}, {4}, {6}, {8}
Vertex figure irr. square pyramid pyramid
Coxeter groups C ~ 4 {\displaystyle {\tilde {C}}_{4}} ,
Properties Vertex transitive

In four-dimensional Euclidean geometry, the stericantitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It is composed of runcitruncated 16-cell, cantitruncated tesseract, rhombicuboctahedral prism, truncated cuboctahedral prism, and 4-8 duoprism facets, arranged around an irregular 5-cell vertex figure.

Related honeycombs

The , , Coxeter group generates 31 permutations of uniform tessellations, 21 with distinct symmetry and 20 with distinct geometry. The expanded tesseractic honeycomb (also known as the stericated tesseractic honeycomb) is geometrically identical to the tesseractic honeycomb. Three of the symmetric honeycombs are shared in the family. Two alternations (13) and (17), and the quarter tesseractic (2) are repeated in other families.

C4 honeycombs
Extended
symmetry 		Extended
diagram 		Order Honeycombs
: ×1

1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13

] ×2 (1), (2), (13), 18
(6), 19, 20
]
↔ ]
↔
↔
↔ 		×6

14, 15, 16, 17

See also

Regular and uniform honeycombs in 4-space:

References

  • Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p. 296, Table II: Regular honeycombs
  • 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,
  • 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". x4x3x3o4x - gicartit - O101
Fundamental convex regular and uniform honeycombs in dimensions 2–9
Space Family A ~ n − 1 {\displaystyle {\tilde {A}}_{n-1}} C ~ n − 1 {\displaystyle {\tilde {C}}_{n-1}} B ~ n − 1 {\displaystyle {\tilde {B}}_{n-1}} D ~ n − 1 {\displaystyle {\tilde {D}}_{n-1}} G ~ 2 {\displaystyle {\tilde {G}}_{2}} / F ~ 4 {\displaystyle {\tilde {F}}_{4}} / E ~ n − 1 {\displaystyle {\tilde {E}}_{n-1}}
E Uniform tiling 0 δ3 hδ3 qδ3 Hexagonal
E Uniform convex honeycomb 0 δ4 hδ4 qδ4
E Uniform 4-honeycomb 0 δ5 hδ5 qδ5 24-cell honeycomb
E Uniform 5-honeycomb 0 δ6 hδ6 qδ6
E Uniform 6-honeycomb 0 δ7 hδ7 qδ7 222
E Uniform 7-honeycomb 0 δ8 hδ8 qδ8 133 • 331
E Uniform 8-honeycomb 0 δ9 hδ9 qδ9 152 • 251 • 521
E Uniform 9-honeycomb 0 δ10 hδ10 qδ10
E Uniform 10-honeycomb 0 δ11 hδ11 qδ11
E Uniform (n-1)-honeycomb 0 δn hδn qδn 1k2 • 2k1 • k21
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