Truncated great icosahedral prism

Truncated great icosahedral prism
(OFF file)
Rank	4
Type	Uniform
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	${\sqrt {\frac {31-9{\sqrt {5}}}{8}}}\approx 1.16594$
Hypervolume	${\frac {125-43{\sqrt {5}}}{4}}\approx 7.21227$
Dichoral angles	Stip–4–hip: $\arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }$
	Tiggy–5/2–stip: 90°
	Tiggy–6–hip: 90°
	Hip–4–hip: $\arccos \left({\frac {\sqrt {5}}{3}}\right)\approx 41.81031^{\circ }$
Height	1
Central density	7
Number of external pieces	1194
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Tiggipe
Dual	Great stellapentakis dodecahedral tegum
Conjugate	Truncated icosahedral prism
Abstract & topological properties
Flag count	2880
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Flag orbits	12
Convex	No
Nature	Tame

The truncated great icosahedral prism (OBSA: 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:

• $\left(0,\,\pm {\frac {1}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1}{2}}\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 1,\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {1}{2}}\right)$.

External links

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

• Klitzing, Richard. "tiggipe".