Small tripesic hecatonicosachoron

Small tripesic hecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sitphi
Coxeter diagram	(o5/2x5x5/2o)/2 (/2)
Elements
Cells	120 truncated great dodecahedra
Faces	720 pentagrams, 720 decagons
Edges	3600
Vertices	600
Vertex figure	Compound of 3 tetragonal disphenoids, edge lengths (√5–1)/2 (base) and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Inradius	$\frac{3+\sqrt5}{4} ≈ 1.30902$
Hypervolume	$165\frac{15+7\sqrt5}{4} ≈ 1264.41463$
Dichoral angles	Tigid–10–tigid: 108°
	Tigid–5/2–tigid: 72°
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Great tripesic hecatonicosachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small tripesic hecatonicosachoron, or sitphi, is a nonconvex noble fissary uniform polychoron that consists of 120 truncated great dodecahedra as cells. 12 cells join at each vertex.

It is fissary due to having a compound vertex figure, specifically a compound of three disphenoids. It shares its edges with the small ditetrahedronary hexacosihecatonicosachoron.

A double cover of this polychoron can be seen as the bitruncated grand stellated hecatonicosachoron.

Cross sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 7: Bitruncates" (#F1).

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#F1).

• Klitzing, Richard. "sitphi".