Quasirhombated icositetrachoron

Quasirhombated icositetrachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Qrico
Coxeter diagram	x3o4/3x3o ()
Elements
Cells	96 triangular prisms, 24 cuboctahedra, 24 quasirhombicuboctahedra
Faces	96+192 triangles, 144+288 squares
Edges	288+576
Vertices	288
Vertex figure	Crossed wedge, edge lengths 1 (two edges of base rectangle and top edge) and √2 (other edges of base rectangle and side edges)
Measures (edge length 1)
Circumradius	${\sqrt {4-2{\sqrt {2}}}}\approx 1.08239$
Hypervolume	$64{\sqrt {2}}-85\approx 5.50967$
Dichoral angles	Querco–3–querco: 120°
	Querco–4–co: 45°
	Querco–4–trip: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
	Co–3–trip: 30°
Related polytopes
Army	Srico, edge length ${\sqrt {2}}-1$
Regiment	Wavaty
Conjugate	Small rhombated icositetrachoron
Convex core	Icositetrachoron
Abstract & topological properties
Flag count	10368
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The quasirhombated icositetrachoron, or qrico, is a nonconvex uniform polychoron that consists of 96 triangular prisms, 24 cuboctahedra and 24 quasirhombicuboctahedra. 2 triangular prisms, 1 cuboctahedron, and 2 quasirhombicuboctahedra join at each vertex. It can be obtained by quasicantellating the icositetrachoron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the sphenoverted trisicositetrachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#229).

• Klitzing, Richard. "qrico".