Small inverted retrosnub icosicosidodecahedral prism

Small inverted retrosnub icosicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sirsiddip
Coxeter diagram	x2s5/2s3/2s3/2*b ()
Elements
Cells	60 triangular prisms, 40 triangular prisms as 20 hexagrammic prisms, 12 pentagrammic prisms, 2 small inverted retrosnub 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	$\frac{\sqrt{17+3\sqrt5-\sqrt{102+46\sqrt5}}}{4} ≈ 0.76629$
Hypervolume	$\frac{45+39\sqrt5-5\sqrt{302+150\sqrt5}}{12} ≈ 0.49764$
Dichoral angles	Sirsid–5/2–stip: 90°
	Sirsid–3–trip: 90°
	Stip–4–trip: $\arccos\left(\sqrt{\frac{15-2\sqrt5-2\sqrt{30\sqrt5-65}}{15}}\right) \approx 44.45753^\circ$
	Trip–4–trip: $\arccos\left(\frac{\sqrt{3+2\sqrt5}}{3}\right) ≈ 24.33196^\circ$
Height	1
Central density	38
Number of pieces	3062
Related polytopes
Army	Semi-uniform Tiddip
Regiment	Sirsiddip
Dual	Small hexagrammic hexecontahedral tegum
Abstract properties
Euler characteristic	–30
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small inverted retrosnub icosicosidodecahedral prism or sirsiddip is a prismatic uniform polychoron that consists of 2 small inverted retrosnub 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 inverted retrosnub icosicosidodecahedron, 1 pentagrammic prism, and 5 triangular prisms. As the name suggests, it is a prism based on the small inverted retrosnub icosicosidodecahedron.

Vertex coordinates

A small inverted retrosnub icosicosidodecahedral prism of edge length 1 has vertex coordinates given by all even permutations of the first three coordinates of:

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#961).

• Klitzing, Richard. "sirsiddip".