Antitruncated great stellated dodecahedron

Antitruncated great stellated dodecahedron
Rank	3
Elements
Faces	20 triangles, 12 propeller stellapods
Edges	60+30
Vertices	60
Related polytopes
Army	Tid
Dual	Antiapiculated great icosahedron
Convex core	Dodecahedron
Abstract & topological properties
Orientable	Yes
Properties
Convex	No
Nature	Tame

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

Vertex coordinates

The coordinates of the antitruncated great stellated dodecahedron are the same as the truncated dodecahedron, being all even permutations of

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

Variations

The antitruncated great stellated dodecahedron is part of a teepee where the great stellated dodecahedron is antitruncated a different amount.