Blend of 2 small rhombidodecahedra

Blend of 2 small rhombidodecahedra
(3D model) (OFF file)
Rank	3
Type	Orbiform
Space	Spherical
Elements
Faces	48 squares, 24 decagons
Edges	24+48+48+96
Vertices	24+24+48
Vertex figures	24+48 butterflies, edge lengths √2 and √(5+√5)/2
	24 (4.10.10)2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11+4\sqrt5}}{2} \approx 2.23295$
Related polytopes
Conjugate	Blend of 2 great rhombidodecahedra
Convex core	Cube, edge length √5
Abstract & topological properties
Flag count	864
Euler characteristic	–48
Orientable	No
Genus	50
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The blend of 2 small rhombidodecahedra is an orbiform polyhedron. It consists of 48 squares and 24 decagons. As the name suggests, it can be constructed by blending two small rhombidodecahedra together by six square faces.

It appears as a cell in the small fusihexacosichoron.

Vertex coordinates

A blend of 2 small rhombidodecahedra of edge length 1 has vertex coordinates given by all permutations of

• $\left(\pm\frac{2+\sqrt5}{2},\,\pm\frac12,\,\pm\frac12\right),$
• $\left(0,\,\pm\frac{3+\sqrt5}{4},\,\pm\frac{5+\sqrt5}{4}\right),$
• $\left(\pm\frac{1+\sqrt5}{4},\,\pm\frac{1+\sqrt5}{2},\,\pm\frac{3+\sqrt5}{4}\right).$

Gallery

A view of the polyhedron with each blend component colored differently.