Small hecatonicosafaceted prismatohecatonicosihexacosichoron

Small hecatonicosafaceted prismatohecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Shif phix
Elements
Cells	600 tetrahedra, 720 pentagonal prisms, 120 small rhombicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagons
Edges	3600+3600
Vertices	2400
Vertex figure	Irregular triangular hemiantipodium, edge lengths 1 (top triangle), (1+√5)/2 (base pseudo-triangle), and √2 (sides)
Measures (edge length 1)
Circumradius	$3+\sqrt5 \approx 5.23607$
Dichoral angles	Srid–4–pip: $\arccos\left(-\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 148.28253°$
	Srid–3–tet: $\arccos\left(\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 22.23876°$
	Srid–5–pip: 18°
Number of external pieces	8880
Level of complexity	24
Related polytopes
Army	Sidpixhi
Regiment	Sidpixhi
Conjugate	Great hecatonicosafaceted prismatohecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	1200
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small hecatonicosafaceted prismatohecatonicosihexacosichoron, or shif phix, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 720 pentagonal prisms, and 120 small rhombicosidodecahedra. One tetrahedron, three pentagonal prisms, and three small rhombicosidodecahedra join at each vertex.

It also has 120 dodecahedra and 1200 triangular prisms as pseudofacets.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#455).