Grand quasirhombic disicositetrachoron

Grand quasirhombic disicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gaquerdy
Elements
Cells	24 great rhombihexahedra, 24 quasitruncated cuboctahedra
Faces	288 squares, 96 hexagons, 144 octagrams
Edges	288+576
Vertices	288
Vertex figure	Crossed butterfly wedge, edge lengths √2 (4), √3 (2), and √2–√2 (4)
Measures (edge length 1)
Circumradius	$\sqrt{4-2\sqrt2} \approx 1.08239$
Dichoral angles	Groh–4–quitco: 90°
	Quitco–6–quitco: 60°
	Groh–8/3–quitco: 45°
Related polytopes
Army	Srico
Regiment	Wavaty
Conjugate	Grand rhombic disicositetrachoron
Convex core	Icositetrachoron
Abstract properties
Euler characteristic	–96
Topological properties
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The grand quasirhombic disicositetrachoron, or gaquerdy, is a nonconvex uniform polychoron that consists of 24 great rhombihexahedra and 24 quasitruncated cuboctahedra. Two great rhombihexahedra and four quasitruncated cuboctahedra join at each vertex.

It can be constructed as the blend of 3 great rhombiprismic tesseractihexadecachora. In the process the cubohemioctahedron cells blend out and the octagrammic prisms blending into great rhombihexahedra.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#232).