Small pentagrammal antiprismatoverted dishecatonicosachoron

Small pentagrammal antiprismatoverted dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Spapivady
Coxeter diagram	(x5o5/2o5x5/3*a)/2
Elements
Cells	120 great dodecahedra, 120 quasitruncated small stellated dodecahedra
Faces	1440 pentagons, 720 decagrams
Edges	3600
Vertices	720
Vertex figure	Pentagrammic antiprism, edge lengths (1+√5)/2 (base) and √(5–√5)/2 (side)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-\sqrt5}{2}} ≈ 1.17557$
Hypervolume	$45\frac{10-\sqrt5}{2} ≈ 174.68847$
Dichoral angles	Quit sissid–10/3–quit sissid: 144°
	Gad–5–quit sissid: 108°
Central density	54
Number of external pieces	32640
Level of complexity	76
Related polytopes
Army	Rox
Regiment	Ragishi
Conjugate	Great pentagonal retroprismatoverted dishecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Euler characteristic	–960
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

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

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#105).

• Klitzing, Richard. "spapivady".