Quasiprismatorhombated grand stellated hecatonicosachoron

{{Infobox polytope The quasiprismatorhombated grand stellated hecatonicosachoron, or quippirgashi, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 720 decagrammic prisms, 120 quasitruncated small stellated dodecahedra, and 120 rhombidodecadodecahedra. 1 pentagrammic prism, 2 decrammic prisms, 1 quasitruncated small stellated dodecahedron, and 1 rhombidodecadodecahedron join at each vertex. It can be obtained by runcitruncating the grand stellated hecatonicosachoron.
 * img = Quippirgashi-slices.gif
 * type=Uniform
 * dim = 4
 * obsa = Quippirgashi
 * off=Quippirgashi.off
 * cells = 720 pentagrammic prisms, 720 decagrammic prisms, 120 quasitruncated small stellated dodecahedra, 120 rhombidodecadodecahedra
 * faces = 3600+3600 squares, 1440 pentagons, 1440 pentagrams, 1440 decagrams
 * edges = 3600+7200+7200
 * vertices = 7200
 * verf = Isosceles trapezoidal pyramid, base edge lengths (1+$\sqrt{5}$)/2, $\sqrt{2}$, ($\sqrt{5}$–1)/2, $\sqrt{2}$; lateral edge lengths $\sqrt{2}$, $\sqrt{2}$, $\sqrt{(5–√5)/2}$, $\sqrt{(5–√5)/2}$
 * coxeter = x5/3x5o5/2x ({{CDD|node_1|5|rat|3x|node_1|5|node|5|rat|2x|node_1}})
 * army=Semi-uniform Prahi
 * reg=Quippirgashi
 * symmetry = H{{sub|4}}, order 14400
 * circum = $$\sqrt{13-5\sqrt5} ≈ 1.34895$$
 * hypervolume = $$45\frac{825-359\sqrt5}{4} ≈ 250.33045$$
 * euler=–960
 * dich= Stip–4–stiddip: $$\arccos\left(-\frac{2\sqrt5}{5}\right) ≈ 153.43495°$$
 * dich2= Quit sissid–10/3–stiddip: 126°
 * dich3= Raded–5–quit sissid: 72°
 * dich4= Raded–4–stiddip: $$\arccos\left(\sqrt{\frac{5-\sqrt5]{10}}\right) ≈ 58.28263°$$
 * dich5= Raded–5/2–stip: 54°
 * conjugate=Prismatorhombated great hecatonicosachoron
 * conv = No
 * orientable=Yes
 * nat=Tame}}

Vertex coordinates
The vertices of a quasiprismatorhombated grand stellated hecatonicosachoron of edge length 1 are given by all permutations of: plus all even permutations of:
 * $$\left(0,\,±(\sqrt5-1),\,±\frac{3-\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{4-\sqrt5}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2},\,±1,\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5}{2},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{4-\sqrt5}{2},\,±\frac{4-\sqrt5}{2},\,±\frac12,\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{3\sqrt5-5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{7-3\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{5-2\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{11-3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(0,\,±3\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±(\sqrt5-2),\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±(\sqrt5-2),\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{5-2\sqrt5}{2},\,±1\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{2\sqrt5-3}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5\sqrt5-7}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{4},\,±(\sqrt5-2),\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{11-3\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±3\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{7-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{2\sqrt5-3}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5}{2},\,±3\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{3\sqrt5-5}{4},\,±(\sqrt5-1)\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{5-\sqrt5}{4},\,±3\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±(\sqrt5-2)\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{7-3\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right).$$

Related polychora
The quasiprismatorhombated grand stellated hecatonicosachoron is the colonel of a three-member regiment that also includes the great prismatohecatonicosidishecatonicosachoron and the great rhombiprismic hecatonicosihecatonicosachoron.