Small snub icosicosidodecahedral prism

Small snub icosicosidodecahedral prism
	(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sesidip
Coxeter diagram	x2s5/2s3s3*b ()
Elements
Cells	60 triangular prisms, 40 triangular prisms as 20 hexagrammic prisms, 12 pentagrammic prisms, 2 small snub icosicosidodecahedra
Faces	120 triangles, 80 triangles as 40 hexagrams, 60+60+60 squares, 24 pentagrams
Edges	60+120+120+120
Vertices	120
Vertex figure	Mirror-symmetric hexagonal pyramid, edge lengths 1, 1, 1, 1, 1, (√5–1)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dihedral angles	Stip–4–trip:
	Trip–4–trip:
	Seside–5/2–stip: 90°
	Seside–3–trip: 90°
Height	1
Central density	2
Number of pieces	214
Related polytopes
Army	Semi-uniform Tipe
Regiment	Sesidip
Dual	Small hexagonal hexecontahedral tegum
Conjugate	Small inverted retrosnub icosicosidodecahedral prism
Abstract properties
Euler characteristic	–30
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small snub icosicosidodecahedral prism or sesidip is a prismatic uniform polychoron that consists of 2 small snub icosicosidodecahedra, 12 pentagrammic prisms, and 40+60 triangular prisms (40 of which form compounds in the same hyperplane, with bases combining into hexagrams). Each vertex joins 1 small snub icosicosidodecahedron, 1 pentagrammic prism, and 5 triangular prisms. As the name suggests, it is a prism based on the small snub icosicosidodecahedron.

Vertex coordinates[edit | edit source]

A small snub icosicosidodecahedral prism of edge length 1 has vertex coordinates given by all even permutations of:

$\left(0,\,±\frac{3+\sqrt{3+2\sqrt5}}{4},\,±\frac{1-\sqrt5+\sqrt{6\sqrt5-2}}{8},\,±\frac12\right),$
$\left(±\frac12,\,±\frac{\sqrt5+\sqrt{3+2\sqrt5}}{4},\,±\frac{\sqrt5-1+\sqrt{6\sqrt5-2}}{8},\,±\frac12\right),$
$\left(±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt{3+2\sqrt5}}{4},\,±\frac{3+\sqrt5+\sqrt{6\sqrt5-2}}{8},\,±\frac12\right).$