Truncated great icosahedral prism

Truncated great icosahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Tiggipe
Coxeter diagram	x o5/2x3x ()
Elements
Cells	12 pentagrammic prisms, 20 hexagonal prisms, 2 truncated great icosahedra
Faces	30+60 squares, 24 pentagrams, 40 hexagons
Edges	60+60+120
Vertices	120
Vertex figure	Sphenoid, edge lengths (√5–1)/2, √3, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{31-9\sqrt5}{8}} ≈ 1.16594$
Hypervolume	$\frac{125-43\sqrt5}{4} ≈ 7.21227$
Dichoral angles	Stip–4–hip: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232^\circ$
	Tiggy–5/2–stip: 90°
	Tiggy–6–hip: 90°
	Hip–4–hip: $\arccos\left(\frac{\sqrt5}{3}\right) ≈ 41.81031^\circ$
Height	1
Central density	7
Number of pieces	1194
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Tiggipe
Dual	Great stellapentakis dodecahedral tegum
Conjugate	Truncated icosahedral prism
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The truncated great icosahedral prism or tiggipe is a prismatic uniform polychoron that consists of 2 truncated great icosahedra, 12 pentagrammic prisms, and 20 hexagonal prisms. Each vertex joins 1 truncated great icosahedron, 1 pentagrammic prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated great icosahedron.

Vertex coordinates

Coordinates for the vertices of a truncated great icosahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\left(0,\,±\frac12,\,±3\frac{\sqrt5-1}{4},\,±\frac12\right),$
• $\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac12\right),$
• $\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{\sqrt5-2}{2},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#904).

• Klitzing, Richard. "tiggipe".