Demicube

A demicube, demihypercube, or half measure polytope is one of an infinite family of convex uniform polytopes. The $n$-dimensional demicube, or simply the $n$-demicube, has $$2^{n-1}$$ vertices. It can be formed by alternation of the $n$-hypercube, making its facets into ($n$-1)-demicube facets and half of its vertex figures into ($n$-1)-simplex facets.

Examples
The demicubes up to 10D are the following:

Vertex coordinates
Coordinates for the vertices of an $n$-demicube with edge length 1 are given by all even sign changes of:
 * ($n$/4, $n$/4, ..., $n$/4).

Measures

 * The circumradius of an $n$-demicube of unit edge length is $$\frac{\sqrt{2n}}4$$.
 * Its height from a demicube facet to the opposite demicube facet is $$\frac{\sqrt2}2$$, regardless of $n$.
 * The angle between two demicube facet hyperplanes is 90°, and the angle between a demicube and a simplex facet hyperplane is $$\arccos\left(-\frac{\sqrt{n}}n\right)$$.