Quasitruncated cuboctahedral prism

Quasitruncated cuboctahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Quitcope
Coxeter diagram	x x4/3x3x ()
Elements
Cells	12 cubes, 8 hexagonal prisms, 6 octagrammic prisms, 2 quasitruncated cuboctahedra
Faces	24+24+24+24 squares, 16 hexagons, 12 octagrams
Edges	48+48+48+48
Vertices	96
Vertex figure	Irregular tetrahedron, edge lengths √2, √3, √2–√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7-3{\sqrt {2}}}{2}}}\approx 1.17417$
Hypervolume	$2\left(11-7{\sqrt {2}}\right)\approx 2.20101$
Dichoral angles	Cube–4–stop: 135°
	Quitco–8/3–stop: 90°
	Quitco–6–hip: 90°
	Quitco–4–cube: 90°
	Hip–4–stop: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
	Cube–4–hip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
Height	1
Central density	-1
Number of external pieces	150
Related polytopes
Army	Semi-uniform Gircope, edge lengths ${\sqrt {2}}-1$ (octagons), $2-{\sqrt {2}}$ (remaining base edges), 1 (sides)
Regiment	Quitcope
Dual	Great disdyakis dodecahedral tegum
Conjugate	Great rhombicuboctahedral prism
Abstract & topological properties
Flag count	2304
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame

The quasitruncated cuboctahedral prism, or quitcope, is a prismatic uniform polychoron that consists of 2 quasitruncated cuboctahedra, 6 octagrammic prisms, 8 hexagonal prisms, and 12 cubes. Each vertex joins one of each type of cell. As the name suggests, it is a prism based on the quasitruncated cuboctahedron.

The quasitruncated cuboctahedral prism can be vertex-inscribed into the great cubihexadecadisoctachoron.

Vertex coordinates

The vertices of a quasitruncated cuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

• $\left(\pm {\frac {2{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#946).

• Klitzing, Richard. "quitcope".