Grand rhombic disicositetrachoron

Grand rhombic disicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gardi
Elements
Cells	24 small rhombihexahedra, 24 great rhombicuboctahedra
Faces	288 squares, 96 hexagons, 144 octagons
Edges	288+576
Vertices	288
Vertex figure	Crossed butterfly wedge, dege lengths √2 (4), √3 (2), and √2+√2 (4)
Measures (edge length 1)
Circumradius	$\sqrt{4+2\sqrt2} \approx 2.61313$
Dichoral angles	Sroh–8–girco: 135°
	Sroh–4–girco: 90°
	Girco–6–girco: 60°
Related polytopes
Army	Srico
Regiment	Srico
Conjugate	Grand quasirhombic disicositetrachoron
Convex core	Icositetrachoron
Abstract properties
Euler characteristic	–96
Topological properties
Orientable	No
Properties
Symmetry	F4, order 1152
Convex	No
Nature	Tame

The grand rhombic disicositetrachoron, or gardi, is a nonconvex uniform polychoron that consists of 24 small rhombihexahedra and 24 great rhombicuboctahedra. Two small rhombihexahedra and four great rhombicuboctahedra join at each vertex.

It can be constructed as the blend of 3 small rhombiprismic tesseractihexadecachora, with the cubohemioctahedron cells blending out and the octagonal prisms blending into small rhombihexahedra.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated icositetrachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#155).