Demicross

The demicross series is a series of quasiregular, semiregular polytopes. A d-dimensional demicross shares all its vertices, edges, and all elements up to ridges (dimension d-2) with the n-dimensional orthoplex. However, it only uses half of the orthoplex's facets, along with d (d-1)-orthoplexes which pass through the center of the polytope. Its vertex figure is the demicross of the previous dimension.

In all dimensions greater than 3, the demicross is uniform. A semi-uniform bowtie formed from faceting a square could be considered to be the 2D demicross.

Vertex coordinates
Coordinates for the vertices of an n-demicross with edge length 1 are given by all permutations of: where the last n–1 entries are zeros.
 * (±$\sqrt{2}$/2, 0, ..., 0),