Antitruncated great icosahedron

Antitruncated great icosahedron
Rank	3
Type	Semi-uniform
Elements
Faces	20 propeller tripods, 12 pentagrams
Edges	60+30
Vertices	60
Related polytopes
Army	Ti
Dual	Antiapiculated great stellated dodecahedron
Convex core	Icosahedron
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Convex	No
Nature	Tame

The antitruncated great icosahedron or inflected truncated great icosahedron is a semi-uniform polyhedron. It is both the antitruncation of the great icosahedron and a faceting of the truncated icosahedron. It consists of 20 propeller tripods and 12 pentagrams, with an isosceles triangle vertex figure and 1 pentagram and 2 propeller tripods at a vertex.

Vertex coordinates

The coordinates of the antitruncated great icosahedron are the same as the truncated icosahedron, being all permutations and changes of sign of

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

Variations

The antitruncated great icosahedron is part of a teepee where the great icosahedron is antitruncated by a different amount.