Great pentagrammal antiprismatoverted dishecatonicosachoron

Great pentagrammal antiprismatoverted dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gippapivady
Coxeter diagram	(x3o5/2o3x5/3*a)/2
Elements
Cells	120 great icosahedra, 120 quasitruncated great stellated dodecahedra
Faces	2400 triangles, 720 decagrams
Edges	3600
Vertices	720
Vertex figure	Pentagrammic antiprism, edge lengths 1 (base) and √(5–√5)/2 (side)
Measures (edge length 1)
Circumradius	$\sqrt{5-2\sqrt5} ≈ 0.72654$
Hypervolume	$25\frac{76-33\sqrt5}{2} ≈ 27.62196$
Dichoral angles	Gike–3–quit gissid: 120°
	Quit gissid–10/3–quit gissid: 108°
Central density	182
Number of external pieces	23040
Level of complexity	46
Related polytopes
Army	Rox
Regiment	Rigfix
Conjugate	Small pentagonal retroprismatoverted dishecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great pentagrammal antiprismatoverted dishecatonicosachoron, or gippapivady, is a nonconvex uniform polychoron that consists of 120 great icosahedra and 120 quasitruncated great stellated dodecahedra. 2 great icosahedra and 10 quasitruncated great stellated dodecahedra join at each vertex.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#120).

• Klitzing, Richard. "gippapivady".