Pentagonal-truncated cubic duoprism

{{Infobox polytope }loc = 30 The pentagonal-truncated cubic duoprism or petic is a convex uniform duoprism that consists of 5 truncated cubic prisms, 6 pentagonal-octagonal duoprisms, and 8 triangular-pentagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-pentagonal duoprism, and 2 pentagonal-octagonal duoprisms.
 * type=Uniform
 * dim = 5
 * img=
 * off = auto
 * obsa = Petic
 * coxeter = x5o x4x3o
 * army = Petic
 * reg = Petic
 * terons = 8 triangular-pentagonal duoprisms, 6 pentagonal-octagonal duoprisms, 5 truncated cubic prisms
 * cells = 40 triangular prisms, 12+24 pentagonal prisms, 30 octagonal prisms, 5 truncated cubes
 * faces = 40 triangles, 60+120 squares, 24 pentagons, 30 octagons
 * edges = 60+120+120
 * vertices = 120
 * circum = $$\sqrt{\frac{45+20\sqrt2+2\sqrt5}{20}} ≈ 1.97176$$
 * hypervol = $$7\frac{\sqrt{425+300\sqrt2+170\sqrt5+120\sqrt{10}}}{12} ≈ 23.39791$$
 * dit1 = Trapedip–pip–podip: $$\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°$$
 * dit2 = Ticcup–tic–ticcup: 108°
 * dit3 = Trapedip–trip–ticcup: 90°
 * dit4 = Podip–op–ticcup: 90°
 * dit5 = Podip–pip–podip: 90°
 * verf = Digonal disphenoidal pyramid, edge lengths 1, $\sqrt{2+√2}$, $\sqrt{2+√2}$ (base triangle), (1+$\sqrt{5}$)/2 (top), $\sqrt{2}$ (side edges)
 * symmetry = BC{{sub|3}}×H{{sub|2}}, order 480
 * pieces = 19
 * dual=Pentagonal-triakis octahedral duotegum
 * conjugate = Pentagrammic-truncated cubic duoprism, Pentagonal-quasitruncated hexahedral duoprism, Pentagrammic-quasitruncated hexahedral duoprism
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

Vertex coordinates
The vertices of a pentagonal-truncated cubic duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 * $$\left(0,\, \sqrt{\frac{5+\sqrt5}{10}},\,±\frac{1+\sqrt2}2,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt{5}}4,\, \sqrt{\frac{5-\sqrt5}{40}},\,±\frac{1+\sqrt2}2,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\, -\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{1+\sqrt2}2,\,±\frac{1+\sqrt2}2,\,±\frac12\right).$$