Rectified grand stellated hecatonicosachoron

Rectified grand stellated hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Ragashi
Coxeter diagram	o5/2x5o5/2o ()
Elements
Cells	120 great dodecahedra, 120 dodecadodecahedra
Faces	1440 pentagons, 720 pentagrams
Edges	3600
Vertices	720
Vertex figure	Semi-uniform pentagrammic prism, edge lengths (1+√5)/2 (base) and (√5–1)/2 (side)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-\sqrt5}{2}} ≈ 1.17557$
Hypervolume	$75\frac{3\sqrt5-4}{2} ≈ 101.55765$
Dichoral angles	Gad–5–did: 108°
	Did–5/2–did: 72°
Central density	66
Number of pieces	37440
Level of complexity	128
Related polytopes
Army	Rox
Regiment	Ragishi
Conjugate	Rectified great hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract properties
Euler characteristic	–960
Topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The rectified grand stellated hecatonicosachoron, or ragashi, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 120 dodecadodecahedra. Two great dodecahedra and five dodecadodecahedra join at each pentagrammic prismatic vertex. As the name suggests, it can be obtained by rectifying the grand stellated hecatonicosachoron.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified great stellated hecatonicosachoron.

Related polytopes

The rectified grand stellated hecatonicosachoron is the base of the 5D scaliform rectified grand stellated hecatonicosachoric alterprism.

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#104).

• Klitzing, Richard. "ragashi".