# Blend of small rhombicosidodecahedron and small rhombidodecahedron

Blend of small rhombicosidodecahedron and small rhombidodecahedron Rank3
TypeOrbiform
SpaceSpherical
Elements
Faces20 triangles, 48 squares, 12 pentagons, 12 decagons
Edges24+48+48+96
Vertices24+24+48
Vertex figures12+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
ConjugateBlend of quasirhombicosidodecahedron and great rhombidodecahedron
Convex coreDodecahedron, edge length (5-5)/2
Abstract & topological properties
Flag count864
Euler characteristic–28
OrientableNo
Genus30
Properties
SymmetryB3/2, order 24
ConvexNo
NatureTame

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: