Truncated tesseractic honeycomb

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In four-dimensional Euclidean geometry, the truncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a truncation of a tesseractic honeycomb creating truncated tesseracts, and adding new 16-cell facets at the original vertices.

Truncated tesseractic honeycomb
(No image)
TypeUniform 4-honeycomb
Schläfli symbolt{4,3,3,4}
t{4,3,31,1}
Coxeter-Dynkin diagram
4-face typetruncated tesseract
16-cell
Cell typeTruncated cube
Tetrahedron
Face type{3}, {8}
Vertex figureoctahedral pyramid
Coxeter group = [4,3,3,4]
= [4,3,31,1]
Dual
Propertiesvertex-transitive

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 ...
C4 honeycombs
Extended
symmetry
Extended
diagram
Order Honeycombs
[4,3,3,4]: ×1

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

[[4,3,3,4]] ×2 (1), (2), (13), 18
(6), 19, 20
[(3,3)[1+,4,3,3,4,1+]]
↔ [(3,3)[31,1,1,1]]
↔ [3,4,3,3]


×6

14, 15, 16, 17

Close

See also

Regular and uniform honeycombs in 4-space:

Notes

References

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