Small disprismatohexacosihecatonicosachoric prism

The small disprismatohexacosihecatonicosachoric prism or sidpixhip is a prismatic uniform polyteron that consists of 2 small disprismatohexacosihecatonicosachora, 120 dodecahedral prisms, 600 tetrahedral prisms, 720 square-pentagonal duoprisms, and 1200 triangular-square duoprisms. 1 small disprismatohexacosihecatonicosachoron, 1 dodecahedral prism, 1 tetrahedral prism, 3 square-pentagonal duoprisms, and 3 triangular-square duoprisms join at each vertex. As the name suggests, it is a prism of the small disprismatohexacosihecatonicosachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a small disprismatohexacosihecatonicosachoric prism of edge length 1 are given by all permutations of the first four coordinates of:

along with the even permutations of the first four coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{9+5\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{3+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{7+3\sqrt5}{4},\,±3\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{9+5\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3+2\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+2\sqrt5}{2},\,±\frac{5+\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±(2+\sqrt5),\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{2},\,±\frac{5+3\sqrt5}{4},\,±\frac{7+3\sqrt5}{4},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{5+2\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±3\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±(2+\sqrt5),\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{2},\,±\frac{7+3\sqrt5}{4},\,±\frac{5+3\sqrt5}{4},\,±\frac12\right).$$