Great pentagonal retroprismatoverted dishecatonicosachoron

Great pentagonal retroprismatoverted dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Giprapivady
Coxeter diagram	(x5x5/2o5o5/3*a)/2
Elements
Cells	120 small stellated dodecahedra, 120 truncated great dodecahedra
Faces	1440 pentagrams, 720 decagons
Edges	3600
Vertices	720
Vertex figure	Pentagonal retroprism, edge lengths (√5–1)/2 (base) and √(5+√5)/2 (side)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5+\sqrt5}{2}} ≈ 1.90211$
Hypervolume	$45\frac{10+\sqrt5}{2} ≈ 275.31153$
Dichoral angles	Tigid–10–tigid: 72°
	Sissid–5/2–tigid: 36°
Central density	126
Number of external pieces	46920
Level of complexity	101
Related polytopes
Army	Rox
Regiment	Righi
Conjugate	Small pentagrammal antiprismatoverted dishecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	–960
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great pentagonal retroprismatoverted dishecatonicosachoron, or giprapivady, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 120 truncated great dodecahedra. 2 small stellated dodecahedra and 10 truncated great dodecahedra join at each vertex.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#91).

• Klitzing, Richard. "giprapivady".