Cantellated tesseractic honeycomb

Cantellated tesseractic honeycomb
(No image)
TypeUniform 4-honeycomb
Schläfli symbolt0,2{4,3,3,4} or rr{4,3,3,4}
rr{4,3,31,1}
Coxeter-Dynkin diagram
4-face typet0,2{4,3,3}
t1{3,3,4}
{3,4}×{}
Cell typeOctahedron
Rhombicuboctahedron
Triangular prism
Face type{3}, {4}
Vertex figureCubic wedge
Coxeter group = [4,3,3,4]
= [4,3,31,1]
Dual
Propertiesvertex-transitive

In four-dimensional Euclidean geometry, the cantellated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a cantellation of a tesseractic honeycomb creating cantellated tesseracts, and new 24-cell and octahedral prism facets at the original vertices.

Related honeycombs

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.

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 3–10 (or 2-9)
    Family / /
    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 133331
    Uniform 9-honeycomb {3[9]} δ9 hδ9 qδ9 152251521
    Uniform 10-honeycomb {3[10]} δ10 hδ10 qδ10
    Uniform n-honeycomb {3[n]} δn hδn qδn 1k22k1k21
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