Misplaced Pages

Steriruncic tesseractic honeycomb

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Steriruncic tesseractic honeycomb
(No image)
Type Uniform honeycomb
Schläfli symbol h3,4{4,3,3,4}
Coxeter-Dynkin diagram =
4-face type r{4,3,4}
t{4,3,4}
t0,1,3{4,3,4}
{3,3}×{}
Cell type t{4,3}
{3,3}
r{4,3}
{3}×{}
t{4}×{}
Face type {8}
{4}
{3}
Vertex figure
Coxeter group B ~ 4 {\displaystyle {\tilde {B}}_{4}} =
Dual ?
Properties vertex-transitive

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

Alternate names

  • Prismatorhombated demitesseractic tetracomb (pirhatit)
  • Great prismatodemitesseractic tetracomb

Related honeycombs

The , , Coxeter group generates 31 permutations of uniform tessellations, 23 with distinct symmetry and 4 with distinct geometry. There are two alternated forms: the alternations (19) and (24) have the same geometry as the 16-cell honeycomb and snub 24-cell honeycomb respectively.

B4 honeycombs
Extended
symmetry 		Extended
diagram 		Order Honeycombs
: ×1

5, 6, 7, 8

<>:
↔
↔ 		×2

9, 10, 11, 12, 13, 14,

(10), 15, 16, (13), 17, 18, 19

]
↔ ]
↔
↔
↔ 		×3

1, 2, 3, 4

]
↔ ]
↔
↔
↔ 		×12

20, 21, 22, 23

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,
  • 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". x3o3o *b3x4x - pirhatit - O110
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
Categories: