10-demicube

In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed.

It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.

Coxeter named this polytope as 171 from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol

Cartesian coordinates for the vertices of a demidekeract centered at the origin are alternate halves of the dekeract: with an odd number of plus signs.

A regular dodecahedron can be embedded as a regular skew polyhedron within the vertices in the 10-demicube, possessing the same symmetries as the 3-dimensional dodecahedron.