Antitruncated cube

The antitruncated cube or inflected truncated cube is a semi-uniform polyhedron. It has 8 triangles and 6 tetrapods as faces and an isosceles triangle as a vertex figure, having one triangle and two tetrapods meeting at each vertex. It is both the antitruncation (sometimes called inflected truncation) of the cube and a faceting of the small rhombicuboctahedron.

It is isomorphic to the truncated cube.

This polyhedron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:$$\sqrt2$$ ≈ 1:1.41421) would yield an octahedron with three stellated squares instead.

Vertex coordinates
The coordinates of the antitruncated cube are shared by that of the rhombicuboctahedron, being all permutations of:


 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12\right).$$

Variations
The antitruncated cube is part of a very similar teepee where the triangles are resized, but the distances between them stay the same.