Antitruncated small stellated dodecahedron

Antitruncated small stellated dodecahedron
Rank	3
Type	Semi-uniform
Elements
Faces	12 pentagons, 12 propeller stellapods
Edges	60+30
Vertices	60
Related polytopes
Army	Ti
Dual	Antiapiculated great dodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Orientable	Yes
Properties
Convex	No
Nature	Tame

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

Vertex coordinates

The coordinates of the antitruncated small stellated dodecahedron 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 small stellated dodecahedron is part of a teepee where the small stellated dodecahedron is antitruncated by a different amount.