Small rhombidodecahedron

Small rhombidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sird
Coxeter diagram	x5/2x5x -12{10/2}
Elements
Faces	30 squares, 12 decagons
Edges	60+60
Vertices	60
Vertex figure	Butterfly, edge lengths √2 and √(5+√5)/2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11+4\sqrt5}}{2} ≈ 2.23295$
Dihedral angles	4–10 #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 density	odd
Number of pieces	150
Level of complexity	10
Related polytopes
Army	Srid
Regiment	Srid
Dual	Small rhombidodecacron
Conjugate	Great rhombidodecahedron
Convex core	Dodecahedron
Abstract properties
Euler characteristic	–18
Topological properties
Orientable	No
Genus	20
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

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.

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#41).

• Klitzing, Richard. "sird".

• Wikipedia Contributors. "Small rhombidodecahedron".
• McCooey, David. "small Rhombidodecahedron"