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Runcicantitruncated tesseractic honeycomb

Tessellation pattern From Wikipedia, the free encyclopedia

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

Runcicantitruncated tesseractic honeycomb
(No image)
TypeUniform 4-honeycomb
Schläfli symbolt0,1,2,3{4,3,3,4}
Coxeter-Dynkin diagram
4-face typeTruncated 24-cell

Truncated octahedral prism
4-8 duoprism
Omnitruncated tesseract

Cell typetruncated cuboctahedron
truncated octahedron
octagonal prism
hexagonal prism
cube
Face type{4}, {6}, {8}
Vertex figureirr. 5-cell
Coxeter group = [4,3,3,4]
= [4,3,31,1]
Dual
Propertiesvertex-transitive
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The [4,3,3,4], , 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 [3,4,3,3] family. Two alternations (13) and (17), and the quarter tesseractic (2) are repeated in other families.

More information C4 honeycombs, Extendedsymmetry ...

The [4,3,31,1], , 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.

More information B4 honeycombs, Extendedsymmetry ...
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See also

Regular and uniform honeycombs in 4-space:

Notes

References

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