Great duoantiprism

The great duoantiprism or gudap, also known as the pentagonal-pentagrammic crossed duoantiprism or 5-5/3 duoantiprism, is a nonconvex uniform polychoron that consists of 50 tetrahedra, 10 pentagonal antiprisms, and 10 pentagrammic retroprisms. 4 tetrahedra, 2 pentagonal antiprisms, and 2 pentagrammic retroprisms join at each vertex.

It is one of only two members of the infinite set of duoantiprisms that can be made uniform, the other being the hexadecachoron. It can be obtained through the process of alternating a non-uniform decagonal-decagrammic duoprism where the decagrams have an edge length of $$\frac{1+\sqrt5}{2}$$ times that of its decagons.

The great duoantiprism contains the vertices of an inscribed pentagonal-pentagrammic duoprism, and in turn can be vertex-inscribed into a small stellated hecatonicosachoron. In fact, it can be derived as a subsymmetric faceting of that polychoron, with the pentagrammic retroprisms being facetings of a ring of 10 small stellated dodecahedral cells and the pentagonal antiprisms being facetings of a ring of 10 great dodecahedral cells.

Vertex coordinates
The coordinates of a great duoantiprism, centered at the origin and with unit edge length, are given by:
 * $$±\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$±\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$±\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$$
 * $$±\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$±\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$±\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$$
 * $$±\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$±\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$±\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$$

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