Prismatoquasirhombated tesseract

Prismatoquasirhombated tesseract
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Paqrit
Coxeter diagram	x4/3o3x3x ()
Elements
Cells	24 cubes, 32 hexagonal prisms, 16 truncated tetrahedra, 8 quasirhombicuboctahedra
Faces	64 triangles, 48+96+96 squares, 64 hexagons
Edges	96+192+192
Vertices	192
Vertex figure	Crossed isosceles trapezoidal pyramid, base edge lengths 1, √2, √2, √2; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7-3{\sqrt {2}}}{2}}}\approx 1.17417$
Hypervolume	$5{\frac {48{\sqrt {2}}-67}{6}}\approx 0.73521$
Dichoral angles	Querco–4–cube: 135°
	Querco–3–tut: 60°
	Querco–4–hip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
	Hip–4–cube: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
	Tut–6–hip: 30°
Related polytopes
Army	Semi-uniform Proh, edge lengths ${\sqrt {2}}-1$ (truncated cubes), $2-{\sqrt {2}}$ (bases of triangular prisms)
Regiment	Gichado
Conjugate	Prismatorhombated tesseract
Abstract & topological properties
Flag count	6144
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The prismatoquasirhombated tesseract, or paqrit, is a nonconvex uniform polychoron that consists of 24 cubes, 32 hexagonal prisms, 16 truncated tetrahedra, and 8 quasirhombicuboctahedra. 1 cube, 2 hexagonal prisms, 1 truncated tetrahedron, and 1 quasirhombicuboctahedron join at each vertex. It can be obtained by quasiruncitruncating the hexadecachoron.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#395).

• Klitzing, Richard. "paqrit".