Grand antiprismatic prism

The grand antiprismatic prism or gappip is a prismatic uniform polyteron that consists of 2 grand antiprisms, 20 pentagonal antiprismatic prisms, and 20+300 tetrahedral prisms. 1 grand antiprism, 2 pentagonal antiprismatic prisms, and 12 tetrahedral prisms join at each vertex. As the name suggests, it can be obtained as a prism based on the grand antiprism, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a grand antiprismatic prism of edge length 1 are given by:
 * $$±\left(±\frac{3+\sqrt5}{4},\,0,\,\frac{1+\sqrt5}{4},\,-\frac12,\,±\frac12\right),$$
 * $$±\left(±\frac12,\,0,\,\frac{3+\sqrt5}{4},\,-\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$±\left(0,\,±\frac{3+\sqrt5}{4},\,\frac12,\,\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$±\left(0,\,±\frac12,\,\frac{1+\sqrt5}{4},\,\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac12\right),$$
 * $$\left(0,\,0,\,0,\,±\frac{1+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,0,\,±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{3+\sqrt5}{4},\,0,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12,\,0,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,0,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,0,\,±\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac12,\,±\frac12\right).$$