Bimesosnub cubic honeycomb

Bimesosnub cubic honeycomb
Rank	4
Type	Isogonal
Space	Euclidean
Elements
Cells	12N sphenoids, 3N tetragonal disphenoids, 4N triangular gyroprisms, N pyritohedral icosahedra
Faces	8N triangles, 12N+12N isosceles triangles, 24N scalene triangles
Edges	6N+6N+24N+24N
Vertices	24N
Vertex figure	14-vertex polyhedron with 2 pentagons, 4 tetragons, and 10 triangles
Measures (based on optimal variant with shortest edge length 1)
Edge lengths	Short edges of pyritohedral icosahedra (6N): 1
	Short lacing edges of triangular gyroprisms (6N): 1
	Long lacing edges of triangular gyroprisms (24N): ${\frac {3{\sqrt {2}}}{2}}\approx 2.12132$
	Edges of equilateral triangles (24N): ${\frac {\sqrt {26}}{2}}\approx 2.54951$
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	(R4×2)/2
Convex	Yes
Nature	Tame

The bimesosnub cubic honeycomb is an isogonal honeycomb that consists of pyritohedral icosahedra, triangular antiprisms, tetragonal disphenoids, and sphenoids. 2 pyritohedral icosahedra, 4 triangular antiprisms, 2 tetragonal disphenoid, and 8 sphenoids join at each vertex. It can be obtained as the convex hull of two opposite bisnub 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 $1:{\frac {\sqrt {26}}{2}}\approx 1:2.54951$.