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:
 * ($\sqrt{2}$/4, $\sqrt{2}$/4, ..., $\sqrt{2}$/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 $$\arccos\left(-\frac{\sqrt{n}}n\right)$$.