Small prismatotrishecatonicosachoron

{{Infobox polytope The small prismatotrishecatonicosachoron, or sipthi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 120 truncated great dodecahedra, 120 great dodecicosidodecahedra, and 120 quasitruncated dodecadodecahedra. 1 triangular prism, 1 truncated great dodecahedron, 1 great dodecicosidodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex.
 * img = Sipthi-slices.gif
 * type=Uniform
 * dim = 4
 * obsa = Sipthi
 * cells = 1200 triangular prisms, 120 truncated great dodecahedra, 120 great dodecicosidodecahedra, 120 quasitruncated dodecadodecahedra
 * faces = 2400 triangles, 3600 squares, 1440 pentagrams, 1440 decagons, 1440 decagrams
 * edges = 3600+7200+7200
 * vertices = 7200
 * verf = Isosceles trapezoidal pyramid, base edge lengths 1, $\sqrt{(5–√5)/2}$, ($\sqrt{5}$–1)/2, $\sqrt{(5–√5)/2}$; lateral edge lengths $\sqrt{2}$, $\sqrt{2}$, $\sqrt{(5+√5)/2}$, $\sqrt{(5+√5)/2}$
 * coxeter = x5x5/2o3x5/3*b ({{CDD|label3|branch_10ru|split2-fp|node_1|5|node_1}})
 * army=Semi-uniform Grix
 * reg=Sipthi
 * symmetry = H{{sub|4}}, order 14400
 * circum = $$\sqrt{8-2\sqrt5} ≈ 1.87826$$
 * hypervolume = $$25\frac{179\sqrt5-251}{4} ≈ 932.85105$$
 * euler=–2040
 * dich= Gaddid–3–trip: 150°
 * dich2= Quitdid–4–trip: $$\arccos\left(\frac{\sqrt3-\sqrt{155}{6}\right) ≈ 110.90516°$$
 * dich3= Gaddid–10/3–quitdid: 108°
 * dich4= Tigid–10–quitdid: 108°
 * dich5= Gaddid–5/2–tigid: 72°
 * conjugate=Great prismatotrishecatonicosachoron
 * conv = No
 * orientable=Yes
 * nat=Tame}}

Vertex coordinates
The vertices of a small prismatotrishecatonicosachoron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(0,\,±1,\,±1,\,±(\sqrt5-1)\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12,\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{5-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5-2}{2},\,±\frac{\sqrt5}{2},\,±\frac32\right),$$
 * $$\left(±\frac{7-\sqrt5}{4},\,±\frac{7-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±3\frac{\sqrt5-1}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac{9-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{\sqrt5}{2},\,±\frac{7-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±\frac{3-\sqrt5}{2},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac12,\,±(\sqrt5-1),\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±1,\,±\frac{3-\sqrt5}{4},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{7-\sqrt5}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±(\sqrt5-1),\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac12,\,±\frac{7-3\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac32,\,±\frac{5-\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{3\sqrt5-5}{4}\right),$$
 * $$\left(±\frac12,\,±1,\,±3\frac{\sqrt5-1}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{9-\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±3\frac{\sqrt5-1}{4},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5-1}{4},\,±\frac{4-\sqrt5}{2},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{5+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac{\sqrt5-2}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac{3\sqrt5-5}{4},\,±\frac32\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5}{2},\,±\frac{3-\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{2\sqrt5-1}{2},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±1,\,±\frac{5-\sqrt5}{4},\,±\frac{\sqrt5-2}{2},\,±\frac{3\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5-1}{2},\,±\frac{5-\sqrt5}{4},\,±\frac{7-\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac32,\,±3\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2}\right).$$

Related polychora
The small prismatotrishecatonicosachoron is the colonel of a 3-member regiment that also includes the prismatoquasirhombated great faceted hexacosichoron and the medial rhombiprismic dishecatonicosachoron.