Great rhombated pentachoric alterprism

The great rhombated pentachoric alterprism or gripa is a convex scaliform polyteron that consists of 2 great rhombated pentachora, 10 truncated tetrahedron atop truncated octahedra, and 20 triangular cupofastegiums. 1 great rhombated pentachoron, 3 truncated tetrahedron atop truncated octahedra, and 2 triangular cupofastegiums join at each vertex. As the name implies, it is a segmentoteron whose bases are 2 great rhombated pentachora in opposite orientation, with the truncated tetrahedra of one base aligned with the truncated octahedra of the other.

It also occurs as a central segment of the small prismated triacontaditeron when seen in small prismatodecachoron-first orientation.

Vertex coordinates
The vertices of a great rhombated pentachoric alterprism of edge length 1 are given by:
 * $$\pm\left(\frac{\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,\frac{\sqrt3}{2},\,\pm\frac32,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,-\sqrt3,\,0,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{\sqrt{10}}{20},\,\frac{5\sqrt6}{12},\,-\frac{\sqrt3}{6},\,\pm\frac32,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{\sqrt{10}}{20},\,\frac{5\sqrt6}{12},\,-\frac{2\sqrt3}{3},\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{\sqrt{10}}{20},\,\frac{5\sqrt6}{12},\,\frac{5\sqrt3}{6},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{\sqrt{10}}{20},\,-\frac{7\sqrt6}{12},\,\frac{\sqrt3}{3},\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{\sqrt{10}}{20},\,-\frac{7\sqrt6}{12},\,-\frac{2\sqrt3}{3},\,0,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{\sqrt{10}}{5},\,0,\,\frac{\sqrt3}{2},\,\pm\frac32,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{\sqrt{10}}{5},\,0,\,-\sqrt3,\,0,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{\sqrt{10}}{5},\,\frac{\sqrt6}{3},\,\frac{\sqrt3}{6},\,\pm\frac32,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{\sqrt{10}}{5},\,\frac{\sqrt6}{3},\,\frac{2\sqrt3}{3},\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{\sqrt{10}}{5},\,\frac{\sqrt6}{3},\,-\frac{5\sqrt3}{6},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{\sqrt{10}}{5},\,-\frac{2\sqrt6}{3},\,\frac{\sqrt3}{6},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{\sqrt{10}}{5},\,-\frac{2\sqrt6}{3},\,-\frac{\sqrt3}{3},\,0,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,\pm\frac32,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,\pm\frac32,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{2\sqrt3}{3},\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{2\sqrt3}{3},\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{5\sqrt3}{6},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{5\sqrt3}{6},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,\pm\frac{\sqrt6}{2},\,0,\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(\frac{3\sqrt{10}}{10},\,\pm\frac{\sqrt6}{2},\,\pm\frac{\sqrt3}{2},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{9\sqrt{10}}{20},\,-\frac{\sqrt6}{12},\,\frac{\sqrt3}{3},\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{9\sqrt{10}}{20},\,-\frac{\sqrt6}{12},\,-\frac{2\sqrt3}{3},\,0,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{9\sqrt{10}}{20},\,\frac{\sqrt6}{4},\,0,\,\pm1,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{9\sqrt{10}}{20},\,\frac{\sqrt6}{4},\,\pm\frac{\sqrt3}{2},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{9\sqrt{10}}{20},\,-\frac{5\sqrt6}{12},\,\frac{\sqrt3}{6},\,\pm\frac12,\,\frac{\sqrt{10}}{10}\right),$$
 * $$\pm\left(-\frac{9\sqrt{10}}{20},\,-\frac{5\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0,\,\frac{\sqrt{10}}{10}\right).$$