# Small rhombidodecahedron

Small rhombidodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSird
Coxeter diagramx5/2x5x -12{10/2}
Elements
Faces30 squares, 12 decagons
Edges60+60
Vertices60
Vertex figureButterfly, edge lengths 2 and (5+5)/2 Measures (edge length 1)
Circumradius$\frac{\sqrt{11+4\sqrt5}}{2} ≈ 2.23295$ Dihedral angles4–10 #1: $\arccos\left(-\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 121.71747^\circ$ 4–10 #2: $\arccos\left(\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 31.71747^\circ$ Central densityodd
Number of external pieces150
Level of complexity10
Related polytopes
ArmySrid
RegimentSrid
DualSmall rhombidodecacron
ConjugateGreat rhombidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–18
OrientableNo
Genus20
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The small rhombidodecahedron, or sird, is a uniform polyhedron. It consists of 30 squares and 12 decagons. Two squares and two decagons meet at each vertex..

It is a faceting of the small rhombicosidodecahedron, using its 30 squares along with the 12 decagons of the small dodecicosidodecahedron.

The truncated dodecadodecahedron (x5/2x5x) is a degenerate polyhedron with 12 decagons, 30 squares, and 12 doubly-wound pentagons. If those pentagons are blended out, the result is the small rhombidodecahedron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small rhombicosidodecahedron.