Small rhombidodecahedron

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..

Small rhombidodecahedron
Rank3
TypeUniform
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
Dihedral angles4–10 #1:
 4–10 #2:
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
Flag orbits4
ConvexNo
NatureTame

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 Edit

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

Representations Edit

A small rhombidodecahedron has representations as two reduced Coxeter diagrams:

  • x5/2x5x -12{10/2}
  • x3/2x5x -20{6/2}

External links Edit