Bicantisnub cubic honeycomb

Bicantisnub cubic honeycomb
Rank	4
Type	Isogonal
Space	Euclidean
Elements
Cells	12N isosceles trapezoidal pyramids, 6N wedges, 4N triangular antiprisms, N pyritohedral icosahedra
Faces	12N+12N+24N isosceles triangles, 8N triangles, 12N isosceles trapezoids, 3N rectangles
Edges	6N+6N+24N+24N
Vertices	12N
Vertex figure	10-vertex polyhedron with 1 pentagon, 3 tetragons, and 7 triangles
Measures (based on optimal variant with shortest edge length 1)
Edge lengths	Short edges of pyritohedral icosahedra (6N): 1
	Lacing edges of triangular antiprisms (24N): 1
	Long edges of rectangles (6N): ${\frac {5+3{\sqrt {101}}}{34}}\approx 1.03381$
	Edges of equilateral triangles (24N): ${\frac {5+3{\sqrt {101}}}{34}}\approx 1.03381$
Abstract & topological properties
Flag count	912N
Orientable	Yes
Properties
Symmetry	(R4/2)×2
Convex	Yes
Nature	Tame

The bicantisnub cubic honeycomb is an isogonal honeycomb that consists of pyritohedral icosahedra, triangular antiprisms, wedges, and isosceles trapezoidal pyramids. 1 pyritohedral icosahedron, 2 triangular antiprisms, 3 wedges, and 5 isosceles trapezoidal pyramids join at each vertex. It can be obtained as the convex hull of two opposite cantic snub cubic honeycombs or by alternating the transitional bicantitruncatocubic honeycomb. It cannot be made scaliform.

A version of this honeycomb with regular icosahedra exists. It has two different edge lengths with a minimum ratio of 1:${\frac {\sqrt {50-10{\sqrt {5}}}}{5}}\approx 1.05146$, though this is not the lowest possible ratio between the longest and shortest edges.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:${\frac {5+3{\sqrt {101}}}{34}}$ ≈ 1:1.03381, and is therefore a near-miss scaliform polyhedral honeycomb. In this variant, none of the cells are regular.