Small rhombidodecahedral prism

Small rhombidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sirdip
Elements
Cells	30 cubes, 12 decagonal prisms, 2 small rhombidodecahedra
Faces	60+60+60 squares, 24 decagons
Edges	60+120+120
Vertices	120
Vertex figure	Butterfly pyramid, edge lengths √2, √(5+√5)/2, √2, √(5+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Dichoral angles	Cube–4–dip #1: $\arccos\left(-\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 121.71747°$
	Sird–4–cube: 90°
	Sird–10–dip: 90°
	Cube–4–dip #2: $\arccos\left(\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 31.71747°$
Height	1
Number of pieces	224
Related polytopes
Army	Sriddip
Regiment	Sriddip
Dual	Small rhombidodecacronic tegum
Conjugate	Great rhombidodecahedral prism
Abstract properties
Euler characteristic	–20
Topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small rhombidodecahedral prism or sirdip is a prismatic uniform polychoron that consists of 2 small rhombidodecahedra, 30 cubes, and 12 decagonal prisms. Each vertex joins 1 small rhombidodecahedron, 2 cubes, and 2 decagonal prisms. As the name suggests, it is a prism based on the small rhombidodecahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#928).