Grand antiprism

The grand antiprism, the pentagonal double antiprismoid, or gap, is a convex uniform polychoron that consists of 300 tetrahedra and 20 pentagonal antiprisms. 12 tetrahedra and 2 pentagonal antiprisms join at each vertex. It may be constructed by taking two orthogonal rings of 10 pentagonal antiprisms each, and connecting them by tetrahedra. Alternatively, one may construct the grand antiprism as a faceting of the hexacosichoron.

Despite the name, the grand antiprism is neither a stellation nor an antiprism in any common sense of the word.

Vertex coordinates
The vertices of a grand antiprism of edge length 1 are given by:


 * ±(±φ, 0, 1, −φ−1),
 * ±(±φ−1, 0, φ, −1),
 * ±(0, ±φ, φ−1, 1),
 * ±(0, ±φ−1, 1, φ),

along with all changes of sign of:


 * (0, 0, 2, 0),
 * (0, 0, 0, 2),
 * (1, 1, 1, 1),
 * (1, 0, φ−1, φ),
 * (0, 1, φ, φ−1),
 * (1, φ−1, φ, 0),
 * (φ, 1, φ−1, 0),
 * (φ−1, φ, 1, 0),
 * (φ, φ−1, 0, 1),
 * (φ−1, 1, 0, φ),
 * (1, φ, 0, φ−1).