Blend of 2 small rhombicosidodecahedra

Blend of 2 small rhombicosidodecahedra
(3D model) (OFF file)
Rank	3
Type	Orbiform
Space	Spherical
Elements
Faces	24 triangles 16 triangles as 8 hexagrams 48 squares 24 pentagons
Edges	24+48+48+96
Vertices	24+24+48
Vertex figures	24 (3.4.5.4)
	48 (6/2.4.5.4)
	24 (5.4.3)2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11+4\sqrt5}}{2} \approx 2.23295$
Central density	0
Number of external pieces	360
Level of complexity	48
Related polytopes
Conjugate	Blend of 2 quasirhombicosidodecahedra
Abstract & topological properties
Flag count	864
Euler characteristic	–8
Orientable	Yes
Genus	5
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The blend of 2 small rhombicosidodecahedra is an orbiform polyhedron. It consists of 40 triangles (16 of which form 8 hexagrams), 48 squares, and 24 pentagons. As the name suggests, it can be constructed by blending two small rhombicosidodecahedra together by six square faces.

It is hollow, and appears as a cell in the small disnub hexacosi-fusihexacosichoron and the small disdishexacosi-fusihexacosichoron.

Vertex coordinates

A blend of 2 small rhombicosidodecahedra 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.