Snub bimesocubic honeycomb
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Snub bimesocubic honeycomb | |
---|---|
Rank | 4 |
Type | Isogonal |
Space | Euclidean |
Elements | |
Cells | 12N sphenoids, 4N triangular antiprisms, N pyritohedral icosahedra |
Faces | 8N triangles, 12N+24N isosceles triangles |
Edges | 3N+12N+24N |
Vertices | 12N |
Vertex figure | 13-vertex polyhedron with 2 pentagons, 4 tetragons, and 8 triangles |
Measures (based on optimal variant with shortest edge length 1) | |
Edge lengths | Edges from diagonals of original squares (3N): 1 |
Edges from diagonals of original isosceles trapezoids (12N): 1 | |
Edges of equilateral triangles (24N): | |
Related polytopes | |
Dual | Semistellated bimesoapiculatocubic honeycomb |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | (R4/2)×2 |
Convex | Yes |
Nature | Tame |
The snub bimesocubic honeycomb is an isogonal honeycomb that consists of pyritohedral icosahedra, triangular antiprisms, and sphenoids. 2 pyritohedral icosahedra, 4 triangular antiprisms, and 8 sphenoids join at each vertex. It can be obtained through the process of alternating the bimesotruncatocubic honeycomb. It cannot be made uniform.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.69293.