Snub bimesocubic honeycomb

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Snub bimesocubic honeycomb
Rank4
TypeIsogonal
SpaceEuclidean
Elements
Cells12N sphenoids, 4N triangular antiprisms, N pyritohedral icosahedra
Faces8N triangles, 12N+24N isosceles triangles
Edges3N+12N+24N
Vertices12N
Vertex figure13-vertex polyhedron with 2 pentagons, 4 tetragons, and 8 triangles
Measures (based on optimal variant with shortest edge length 1)
Edge lengthsEdges from diagonals of original squares (3N): 1
 Edges from diagonals of original isosceles trapezoids (12N): 1
 Edges of equilateral triangles (24N):
Related polytopes
DualSemistellated bimesoapiculatocubic honeycomb
Abstract & topological properties
OrientableYes
Properties
Symmetry(R4/2)×2
ConvexYes
NatureTame

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.