# Blend of 2 small rhombicosidodecahedra

Blend of 2 small rhombicosidodecahedra Rank3
TypeOrbiform
SpaceSpherical
Elements
Faces24 triangles
16 triangles as 8 hexagrams
48 squares
24 pentagons
Edges24+48+48+96
Vertices24+24+48
Vertex figures24 (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 density0
Number of external pieces360
Level of complexity48
Related polytopes
ConjugateBlend of 2 quasirhombicosidodecahedra
Abstract & topological properties
Flag count864
Euler characteristic–8
OrientableYes
Genus5
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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

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