Steriruncic tesseractic honeycomb

Steriruncic tesseractic honeycomb
(No image)
TypeUniform honeycomb
Schläfli symbolh3,4{4,3,3,4}
Coxeter-Dynkin diagram =
4-face typer{4,3,4}
t{4,3,4}
t0,1,3{4,3,4}
{3,3}×{}
Cell typet{4,3}
{3,3}
r{4,3}
{3}×{}
t{4}×{}
Face type{8}
{4}
{3}
Vertex figure
Coxeter group{\tilde{B}}_4 = [4,3,31,1]
Dual?
Propertiesvertex-transitive

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

Alternate names

Related honeycombs

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.

See also

Regular and uniform honeycombs in 4-space:

Notes

    References

    Fundamental convex regular and uniform honeycombs in dimensions 2–10
    Family {\tilde{A}}_{n-1} {\tilde{C}}_{n-1} {\tilde{B}}_{n-1} {\tilde{D}}_{n-1} {\tilde{G}}_2 / {\tilde{F}}_4 / {\tilde{E}}_{n-1}
    Uniform tiling {3[3]} δ3 hδ3 qδ3 Hexagonal
    Uniform convex honeycomb {3[4]} δ4 hδ4 qδ4
    Uniform 5-honeycomb {3[5]} δ5 hδ5 qδ5 24-cell honeycomb
    Uniform 6-honeycomb {3[6]} δ6 hδ6 qδ6
    Uniform 7-honeycomb {3[7]} δ7 hδ7 qδ7 222
    Uniform 8-honeycomb {3[8]} δ8 hδ8 qδ8 133 • 331
    Uniform 9-honeycomb {3[9]} δ9 hδ9 qδ9 152 • 251 • 521
    Uniform n-honeycomb {3[n]} δn hδn qδn 1k2 • 2k1 • k21
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