Quasirhombicuboctahedral prism

Quasirhombicuboctahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quercope
Coxeter diagram	x x4/3o3x ()
Elements
Cells	8 triangular prisms, 6+12 cubes, 2 quasirhombicuboctahedra
Faces	16 triangles, 12+24+24+24 squares
Edges	24+48+48
Vertices	48
Vertex figure	Crossed isosceles trapezoidal pyramid, edge lengths 1, √2, √2, √2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045$
Hypervolume	$2\frac{5\sqrt2-6}{3} ≈ 0.71404$
Dichoral angles	Querco–4–cube: 90°
	Querco–3–trip: 90°
	Cube–4–cube: 45°
	Trip–4–cube: $\arccos\left(\frac{\sqrt6}{3}\right) ≈ 35.26439^\circ$
Height	1
Central density	5
Number of pieces	490
Related polytopes
Army	Semi-uniform Ticcup
Regiment	Goccope
Dual	Great deltoidal icositetrahedral tegum
Conjugate	Small rhombicuboctahedral prism
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame
Discovered by	{{{discoverer}}}

The quasirhombicuboctahedral prism or quercope is a prismatic uniform polychoron that consists of 2 quasirhombicuboctahedra, 6+12 cubes, and 8 triangular prisms. Each vertex joins 1 quasirhombicuboctahedron, 1 triangular prism, and 3 cubes. As the name suggests, it is a prism based on the quasirhombicuboctahedron.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#933).

• Klitzing, Richard. "quercope".