Small dodecahemidodecahedral prism

Small dodecahemidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sidhiddip
Coxeter diagram	/2 ((x x5/4o5x5*b)/2)
Elements
Cells	12 pentagonal prisms, 6 decagonal prisms, 2 small dodecahemidodecahedra
Faces	60 squares, 24 pentagons, 12 decagons
Edges	30+120
Vertices	60
Vertex figure	Bowtie pyramid, edge lengths (1+√5)/2, √(5+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{7+2\sqrt5}}{2} ≈ 1.69353$
Dichoral angles	Sidhid–5–pip: 90°
	Sidhid–10–dip: 90°
	Pip–4–dip: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495^\circ$
Height	1
Number of pieces	96
Related polytopes
Army	Iddip
Regiment	Iddip
Dual	Small dodecahemidodecacronic tegum
Conjugate	Great dodecahemidodecahedral prism
Abstract properties
Euler characteristic	–14
Topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small dodecahemidodecahedral prism or sidhiddip, is a prismatic uniform polychoron that consists of 2 small dodecahemidodecahedra, 12 pentagonal prisms, and 6 decagonal prisms. Each vertex joins 1 small dodecahemidodecahedron, 2 pentagonal prisms, and 2 decagonal prisms. As the name suggests, it is a prism based on the small dodecahemidodecahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#912).