Small quasidisprismatohexacosihecatonicosachoron

Small quasidisprismatohexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Saquid paxhi
Coxeter diagram	x5o3o3/2x ()
Elements
Cells	600 tetrahedra, 1200 triangular prisms, 720 pentagonal prisms, 120 dodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagons
Edges	3600
Vertices	600
Vertex figure	Compound of 4 triangular retroantipodiums, edge lengths 1 (small base), (1+√5)/2 (large base), and √2 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Hypervolume	$5\frac{22\sqrt5-35}{4} ≈ 17.74187$
Dichoral angles	Doe–5–pip: 18°
	Pip–4–trip: $\arccos\left(\sqrt{\frac{10+2\sqrt5}{15}}\right) ≈ 10.81232^\circ$
	Tet–3–trip: $\arccos\left(\frac{\sqrt6+\sqrt{30}}{8}\right) ≈ 7.76124^\circ$
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Quasidisprismatogrand hexacosihecatonicosachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Feral

The small quasidisprismatohexacosihecatonicosachoron, or saquid paxhi, is a nonconvex fissary uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, 1200 triangular prisms, and 720 pentagonal prisms. 4 tetrahedra, 4 dodecahedra, 12 triangular prisms, and 12 pentagonal prisms join at each vertex. It is the result of pushing the cells of either a hecatonicosachoron or a hexacosichoron inwards.

It is fissary as vertices coincide by four, producing a compound vertex figure; in addition, edges coincide by two.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#F11).

• Klitzing, Richard. "saquid paxhi".