# Blend of 2 small rhombidodecahedra

Blend of 2 small rhombidodecahedra
Rank3
TypeOrbiform
Elements
Faces48 squares, 24 decagons
Edges24+48+48+96
Vertices24+24+48
Vertex figures24+48 butterflies, edge lengths 2 and (5+5)/2
24 (4.10.10)2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {11+4{\sqrt {5}}}}{2}}\approx 2.23295}$
Related polytopes
ConjugateBlend of 2 great rhombidodecahedra
Convex coreCube, edge length 5
Abstract & topological properties
Flag count864
Euler characteristic–48
OrientableNo
Genus50
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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

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