Biprismatosnub cubic honeycomb
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| Biprismatosnub cubic honeycomb | |
|---|---|
| Rank | 4 |
| Type | Isogonal |
| Space | Euclidean |
| Elements | |
| Cells | 12N sphenoids, 6N rhombic disphenoids, 3N tetragonal disphenoids, N tetrahedra, 2N triangular antiprisms |
| Faces | 24N scalene triangles, 12N+12N isosceles triangles, 4N triangles |
| Edges | 2N+6N+12N+12N |
| Vertices | 4N |
| Vertex figure | 16-vertex polyhedron with 3 tetragons and 22 triangles |
| Measures (based on optimal variant with shortest edge length 1) | |
| Edge lengths | Edges of regular tetrahedra (6N): 1 |
| Edges between two opposite regular tetrahedra (2N): 1 | |
| Lacing edges of triangular antiprisms (12N): | |
| Lacing edges of tetragonal disphenoids (12N): | |
| Related polytopes | |
| Dual | Bisemistellated crystallocubic honeycomb |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | P4×2 |
| Convex | Yes |
| Nature | Tame |
The biprismatosnub cubic honeycomb is an isogonal honeycomb that consists of triangular antiprisms, tetrahedra, tetragonal disphenoids, rhombic disphenoids, and sphenoids. 3 triangular antiprisms, 1 tetrahedron, 3 tetragonal disphenoids, 6 rhombic disphenoids, and 12 sphenoids join at each vertex. It can be obtained as the convex hull of two opposite prismatosnub cubic honeycombs with regular symmetry. It cannot be made uniform.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:.
