Great snub dodecicosidodecahedral prism

Great snub dodecicosidodecahedral prism
	(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gisdiddip
Coxeter diagram	x2s5/3s5/2s3*b ()
Elements
Cells	20+60 triangular prisms, 24 pentagrammic prisms, 2 great snub dodecicosidodecahedra
Faces	40+120 triangles, 60+60+60 squares, 48 pentagrams
Edges	60+120+120+120
Vertices	120
Vertex figure	Irregular hexagonal pyramid, edge lengths 1, 1, 1, (√5–1)/2, 1, (√5–1)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stip–4–trip #1:
	Trip–4–trip:
	Gisdid–5/2–stip: 90°
	Gisdid–3–trip: 90°
	Stip–4–trip #2:
Height	1
Central density	10
Number of pieces	602
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Gisdiddip
Dual	Great hexagonal hexecontahedral tegum
Abstract properties
Euler characteristic	–18
Topological properties
Orientable	Yes
Properties
Symmetry	H3+×A1, order 120
Convex	No
Nature	Tame
Discovered by	{{{discoverer}}}

The great snub dodecicosidodecahedral prism or gisdiddip is a prismatic uniform polychoron that consists of 2 great snub dodecicosidodecahedra, 24 pentagrammic prisms (which form compounds in the same hyperplane), and 20+60 triangular prisms. Each vertex joins 1 great snub dodecicosidodecahedron,2 pentagrammic prisms, and 4 triangular prisms. As the name suggests, it is a prism based on the great snub dodecicosidodecahedron.

Vertex coordinates[edit | edit source]

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

$\left(±\sqrt{\frac{\sqrt5-1-2\sqrt{\sqrt5-2}}{2}},\,±\sqrt{\frac{3-\sqrt5-\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2+\sqrt{2\sqrt5-2}}{8}},\,±\frac12\right),$
$\left(0,\,±\frac{\sqrt{3-\sqrt5}}{2},\,±\frac{\sqrt{\sqrt5-1}}{2},\,±\frac12\right),$
$\left(±\sqrt{\frac{3-\sqrt5+\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2-\sqrt{2\sqrt5-2}}{8}},\,±\sqrt{\frac{\sqrt5-1+2\sqrt{\sqrt5-2}}{8}},\,±\frac12\right).$