Small icosicosidodecahedral prism

Small icosicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Siidip
Coxeter diagram	x x5/2o3x3*b ()
Elements
Cells	20 triangular prisms, 12 pentagrammic prisms, 20 hexagonal prisms, 2 small icosicosidodecahedra
Faces	40 triangles, 60+60 squares, 24 pentagrams, 40 hexagons
Edges	60+120+120
Vertices	120
Vertex figure	Isosceles trapezoidal pyramid, edge lengths 1, √3, (√5–1)/2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{19+3\sqrt5}{8}} ≈ 1.79263$
Hypervolume	$\frac{3)+29\sqrt5}{3} ≈ 31.61533$
Dichoral angles	Stip–4–hip: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°$
	Trip–4–hip: $\arccos\left(-\frac{\sqrt5}{3}\right) ≈ 138.18969°$
	Siid–5/2–stip: 90°
	Siid–3–trip: 90°
	Siid–6–hip: 90°
Height	1
Central density	2
Number of pieces	94
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Siidip
Dual	Small icosacronic hexecontahedral tegum
Conjugate	Great icosicosidodecahedral prism
Abstract properties
Euler characteristic	–10
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small icosicosidodecahedral prism or siidip is a prismatic uniform polychoron that consists of 2 small icosicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 20 hexagonal prisms. Each vertex joins 1 small icosicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the small icosicosidodecahedron.

Vertex coordinates

The vertices of a small icosicosidodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac12\right),$
• $\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac12\right),$
• $\left(±\frac12,\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#941).

• Klitzing, Richard. "siidip".