Small quasidisprismatohexacosihecatonicosachoron

Small quasidisprismatohexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
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	${\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825$
Hypervolume	$5{\frac {22{\sqrt {5}}-35}{4}}\approx 17.74187$
Dichoral angles	Doe–5–pip: 18°
	Pip–4–trip: $\arccos \left({\sqrt {\frac {10+2{\sqrt {5}}}{15}}}\right)\approx 10.81232^{\circ }$
	Tet–3–trip: $\arccos \left({\frac {{\sqrt {6}}+{\sqrt {30}}}{8}}\right)\approx 7.76124^{\circ }$
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".