Small rhombated pentachoric alterprism

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

It can also be constructed as a diminishing of the penteractitriacontaditeron when seen in rectified pentachoron-first orientation. In fact 2 rectified pentachoron atop small rhombated pentachoron segmentotera can be cut off from the penteractitriacontaditeron to produce this segmentoteron. The triangular antifastegiums are parts of remaining rectified pentachoron facets, while the octahedron atop cuboctahedron laterals are halves of icositetrachoron facets.

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

Much simpler coordinates can be given by all permutations of:


 * $$±\left(\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,-\frac{\sqrt2}{2},\,0,\,0\right).$$