Small icosihemidodecahedral prism

Small icosihemidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Seihiddip
Coxeter diagram	(x x3/2o3x5*b)/2 ()
Elements
Cells	20 triangular prisms, 6 decagonal prisms, 2 small icosihemidodecahedra
Faces	40 triangles, 60 squares, 12 decagons
Edges	30+120
Vertices	60
Vertex figure	Bowtie pyramid, edge lengths 1, √(5+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{7+2\sqrt5}}{2} ≈ 1.69353$
Dichoral angles	Seihid–3–trip: 90°
	Seihid–10–dip: 90°
	Trip–4–dip: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768°$
Height	1
Number of pieces	120
Related polytopes
Army	Iddip
Regiment	Iddip
Dual	Small icosihemidodecacronic tegum
Conjugate	Great icosihemidodecahedral prism
Abstract properties
Euler characteristic	–6
Topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small icosihemidodecahedral prism or seihiddip, is a prismatic uniform polychoron that consists of 2 small icosihemidodecahedra, 20 triangular prisms, and 6 decagonal prisms. Each vertex joins 1 small icosihemidodecahedron, 2 triangular prisms, and 2 decagonal prisms. As the name suggests, it is a prism based on the small icosihemidodecahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#913).