Rhombic great hecatonicosihexacosichoron

Rhombic great hecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Raghix
Elements
Cells	1200 triangular prisms, 600 truncated tetrahedra, 120 rhombicosahedra
Faces	2400 triangles, 3600 squares, 2400 hexagons
Edges	3600+7200
Vertices	3600
Vertex figure	Butterfly wedge, edge lengths 1 (bases), √2 (sides of outer triangles), and √3 (sides of inner triangles)
Measures (edge length 1)
Circumradius	${\frac {{\sqrt {30}}-{\sqrt {6}}}{2}}\approx 1.51387$
Dichoral angles	Tut–3–trip: $\arccos \left({\frac {{\sqrt {6}}-{\sqrt {30}}}{8}}\right)\approx 112.23876^{\circ }$
	Ri–4–trip: $\arccos \left({\frac {{\sqrt {3}}-{\sqrt {15}}}{6}}\right)\approx 110.90516^{\circ }$
	Ri–6–tut: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
Related polytopes
Army	Semi-uniform xhi
Regiment	Sirgaghi
Conjugate	Rhombic small hecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	–720
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The rhombic great hecatonicosihexacosichoron, or raghix, is a nonconvex uniform polychoron that consists of 600 truncated tetrahedra, 120 rhombicosahedra, and 1200 triangular prisms. 2 of each type of cell join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated great grand hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#202).