Prismatoquasirhombated icositetrachoron

Prismatoquasirhombated icositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Paqri
Coxeter diagram	x3x4/3o3x ()
Elements
Cells	96 triangular prisms, 96 hexagonal prisms, 24 truncated octahedra, 24 quasirhombicuboctahedra
Faces	192 triangles, 144+288+288 squares, 192 hexagons
Edges	288+576+576
Vertices	576
Vertex figure	Crossed isosceles trapezoidal pyramid, base edge lengths 1, √2, √2, √2; lateral edge lengths √3, √3, √2, √2
Measures (edge length 1)
Circumradius	${\sqrt {8-3{\sqrt {2}}}}\approx 1.93839$
Hypervolume	$224{\sqrt {2}}-305\approx 11.78384$
Dichoral angles	Querco–3–trip: 150°
	Querco–4–toe: 45°
	Querco–4–hip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
	Toe–6–hip: 30°
	Hip–4–trip: $\arccos \left({\frac {2{\sqrt {2}}}{3}}\right)\approx 19.47122^{\circ }$
Related polytopes
Army	Semi-uniform Grico, edge lengths ${\sqrt {2}}-1$ (truncated cubes), $2-{\sqrt {2}}$ (sides of triangular prisms)
Regiment	Gipti
Conjugate	Prismatorhombated icositetrachoron
Abstract & topological properties
Flag count	18432
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The prismatoquasirhombated icositetrachoron, or paqri, is a nonconvex uniform polychoron that consists of 96 triangular prisms, 96 hexagonal prisms, 24 truncated octahedra, and 24 quasirhombicuboctahedra. 1 triangular prism, 2 hexagonal prisms, 1 truncated octahedron, and 1 quasirhombicuboctahedron join at each vertex. It can be obtained by quasiruncitruncating the icositetrachoron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great prismatotrisicositetrachoron.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#398).

• Klitzing, Richard. "paqri".