# Antitruncated great icosahedron

Antitruncated great icosahedron
Rank3
TypeSemi-uniform
Elements
Faces20 propeller tripods, 12 pentagrams
Edges60+30
Vertices60
Related polytopes
ArmyTi
DualAntiapiculated great stellated dodecahedron
Convex coreIcosahedron
Abstract & topological properties
Euler characteristic2
OrientableYes
Genus0
Properties
ConvexNo
NatureTame

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

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

## Variations

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