Blend of small rhombicosidodecahedron and small rhombidodecahedron

Blend of small rhombicosidodecahedron and small rhombidodecahedron
(3D model) (OFF file)
Rank	3
Type	Orbiform
Space	Spherical
Elements
Faces	20 triangles, 48 squares, 12 pentagons, 12 decagons
Edges	24+48+48+96
Vertices	24+24+48
Vertex figures	12+24 isosceles trapezoids, edge lengths 1, √2, (1+√5)/2, √2
	12+24 butterflies, edge lengths √2 and √(5+√5)/2
	24 (3.4.5.10.4.10)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11+4\sqrt5}}{2} \approx 2.23295$
Related polytopes
Conjugate	Blend of quasirhombicosidodecahedron and great rhombidodecahedron
Convex core	Dodecahedron, edge length (5-√5)/2
Abstract & topological properties
Flag count	864
Euler characteristic	–28
Orientable	No
Genus	30
Properties
Symmetry	B3/2, order 24
Convex	No
Nature	Tame

The blend of small rhombicosidodecahedron and small rhombidodecahedron is an orbiform polyhedron. It consists of 20 triangles, 48 squares, 12 pentagons, and 12 decagons. As the name suggests, it can be constructed by blending a small rhombicosidodecahedron and a small rhombidodecahedron together by six square faces.

Vertex coordinates

A blend of small rhombicosidodecahedron and small rhombidodecahedron of edge length 1 has vertex coordinates given by all permutations of

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

Related polytopes

The blend of small rhombicosidodecahedron and small rhombidodecahedron appears as a cell in several scaliform polychora. These include the:

• small snub hexacosifusihexacosichoron
• small dishexacosifusihexacosichoron
• small hexacosihexacosifusihexacosichoron
• small fusihexacosidishexacosichoron
• small disnub dishexacosifusihexacosichoron