Antitruncated great dodecahedron

Antitruncated great dodecahedron
Rank	3
Type	Semi-uniform
Elements
Faces	12 pentagrams, 12 pentapods.
Edges	60+30
Vertices	60
Related polytopes
Army	Srid
Dual	Antiapiculated small stellated dodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Euler characteristic	-6
Orientable	Yes
Genus	4
Properties
Convex	No
Nature	Tame

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

Vertex coordinates

The coordinates of the antitruncated great dodecahedron are the same as the small rhombicosidodecahedron, being

all permutations of

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

along with all even permutations of

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

Variations

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