# Hypertruncated cube

Hypertruncated cube
Rank3
Elements
Faces8 triangles, 6 tetrapods
Edges12+24
Vertices24
Measures (edge length 1)
Central density1
Related polytopes
DualConcave triakis octahedron
ConjugateAntitruncated cube
Abstract & topological properties
OrientableYes
Properties
SymmetryBC3, order 48
NatureTame

The hypertruncated cube is a semi-uniform polyhedron. It consists of 8 triangles and 6 tetrapods and has 1 triangle and 2 tetrapods at a vertex. It is very similar to the antitruncated cube, the only difference being that the triangles connect to the larger sides of tetrapods in the hypertruncated cube, and the smaller sides in the antitruncated cube. The hypertruncated cube is both the hypertruncation of the cube and a faceting of the truncated cube.

## Vertex coordinates

The hypertruncated cube shares its vertices with the truncated cube, being all permutations of:

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

## Variations

A teepee of semi-uniform polyhedra can be formed by adjusting the size of the tetrapods.