Rhombic great dishecatonicosachoron

The rhombic great dishecatonicosachoron, or raggady, is a nonconvex uniform polychoron that consists of 120 truncated great icosahedra, 120 rhombicosahedra, and 720 pentagrammic prisms. 2 of each type of cell join at each vertex.

Rhombic great dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Raggady
Elements
Cells	720 pentagrammic prisms, 120 truncated great icosahedra, 120 rhombicosahedra
Faces	3600 squares, 1440 pentagrams, 2400 hexagons
Edges	3600+7200
Vertices	3600
Vertex figure	Butterfly wedge, edge lengths (√5–1)/2 (bases), Template:Radci (sides of outer triangles), and √3 (sides of inner triangles)
Measures (edge length 1)
Circumradius	${\sqrt {7-2{\sqrt {5}}}}\approx 1.58993$
Dichoral angles	Tiggy–5/2–stip: 126°
	Ri–4–stip: $\arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }$
	Ri–6–tiggy: 60°
Related polytopes
Army	Srahi
Regiment	Sirgashi
Conjugate	Rhombic small dishecatonicosachoron
Abstract & topological properties
Euler characteristic	–720
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#209).