Antitruncated octahedron

Antitruncated octahedron
Rank	3
Type	Semi-uniform
Space	Spherical
Elements
Faces	6 squares, 8 tripods
Edges	12+24
Vertices	24
Measures (edge length 1)
Central density	1
Related polytopes
Army	Toe
Dual	Antiapiculated cube
Convex core	Octahedron
Abstract & topological properties
Orientable	Yes
Properties
Convex	No
Nature	Tame

The antitruncated octahedron or inflected truncated octahedron is a semi-uniform polyhedron. It consists of 6 squares and 8 tripods. It has 1 square and 2 tripods at a vertex, and an isosceles triangle as a vertex. It is both the anitruncation (or inflected truncation) of the octahedron and a faceting of the truncated octahedron.

Vertex coordinates

The coordinates of the antitruncated octahedron are the same as the truncated octahedron, being all permutations of

• $\left(±\sqrt2,\,±\frac{\sqrt2}{2},\,0\right).$

Variations

The antitruncated octahedron is part of a teepee where the squares are resized.