Triacontaditeron

The triacontaditeron, or tac, also called the pentacross, 5-orthoplex, or square-octahedral duopyramid, is one of the 3 regular polytera. It has 32 regular pentachora as facets, joining 16 to a vertex in an hexadecachoral arrangement. It is the 5-dimensional orthoplex.

Vertex coordinates
The vertices of a regular triacontaditeron of edge length 1, centered at the origin, are given by all permutations of:
 * (±$\sqrt{2}$/2, 0, 0, 0, 0).