Quasiprismatohecatonicosachoron

Quasiprismatohecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quiphi
Coxeter diagram	(x5/2o5o5/3x)/2 (/2)
Elements
Cells	720 pentagrammic prisms, 120 small stellated dodecahedra
Faces	1800 squares, 1440 pentagrams
Edges	3600
Vertices	720
Vertex figure	Pentagonal retroprism, edge lengths (√5–1)/2 (base) and √2 (side)
Measures (edge length 1)
Circumradius	$\sqrt{5-2\sqrt5} ≈ 0.72654$
Hypervolume	$15\frac{155-69\sqrt5}{4} ≈ 2.66741$
Dichoral angles	Sissid–5/2–stip: 54°
	Stip–4–stip: $\arccos\left(\frac{2\sqrt5}{5}\right) ≈ 26.56505^\circ$
Central density	–505
Number of external pieces	767040
Level of complexity	2423
Related polytopes
Army	Rox
Regiment	Rigfix
Conjugate	Small prismatohecatonicosachoron
Convex core	Joined hexacosichoron
Abstract & topological properties
Euler characteristic	–480
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The quasiprismatohecatonicosachoron, or quiphi, is a nonconvex uniform polychoron that consists of 120 small stellated dodecahedra and 720 pentagrammic prisms. 2 small stellated dodecahedra and 10 pentagrammic prisms join at each vertex.

It is in the same regiment as the rectified great faceted hexacosichoron.

A double cover of this polychoron can be formed by pushing the cells of the grand stellated hecatonicosachoron inward.

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" (#121).

• Klitzing, Richard. "quiphi".