Great icosicosidodecahedral prism

Great icosicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Giidip
Coxeter diagram	x o3/2x3x5*b ()
Elements
Cells	20 triangular prisms, 12 pentagonal prisms, 20 hexagonal prisms, 2 great icosicosidodecahedra
Faces	40 triangles, 60+60 squares, 24 pentagons, 40 hexagons
Edges	60+120+120
Vertices	120
Vertex figure	Crossed isosceles trapezoidal pyramid, edge lengths 1, √3, (1+√5)/2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{19-3\sqrt5}{8}} ≈ 1.23955$
Hypervolume	$\frac{29\sqrt5-30}{3} ≈ 11.61533$
Dichoral angles	Pip–4–hip: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232^\circ$
	Giid–5–pip: 90°
	Giid–3–trip: 90°
	Giid–6–hip: 90°
	Trip–4–hip: $\arccos\left(\frac{\sqrt5}{3}\right) ≈ 41.81031^\circ$
Height	1
Central density	6
Number of external pieces	1234
Related polytopes
Army	Semi-uniform Tiddip
Regiment	Gidditdiddip
Dual	Great icosacronic hexecontahedral bipyramid
Conjugate	Small icosicosidodecahedral prism
Abstract & topological properties
Euler characteristic	–10
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

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

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great ditrigonal dodecicosidodecahedral prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#936).

• Klitzing, Richard. "giidip".