Small dodecahemicosahedral prism

Small dodecahemicosahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sidhipe
Coxeter diagram	/2 ((x x5/3o5/2x3*b)/2)
Elements
Cells	12 pentagrammic prisms, 10 hexagonal prisms, 2 small dodecahemicosahedra
Faces	60 squares, 24 pentagrams, 20 hexagons
Edges	30+120
Vertices	60
Vertex figure	Bowtie pyramid, edge lengths (√5–1)/2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt5}{2} ≈ 1.11803$
Dichoral angles	Sidhei–5/2–stip: 90°
	Sidhei–6–hip: 90°
	Stip–4–hip: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768^\circ$
Height	1
Number of pieces	156
Related polytopes
Army	Semi-uniform Iddip
Regiment	Diddip
Dual	Small dodecahemicosacronic tegum
Conjugate	Great dodecahemicosahedral prism
Abstract properties
Euler characteristic	–10
Topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small dodecahemicosahedral prism or sidhipe, is a prismatic uniform polychoron that consists of 2 small dodecahemicosahedra, 12 pentagrammic prisms, and 10 hexagonal prisms. Each vertex joins 1 small dodecahemicosahedron, 2 pentagrammic prisms, and 2 hexagonal prisms. As the name suggests, it is a prism based on the small dodecahemicosahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#915).