Great hecatonicosafaceted prismatohecatonicosihexacosichoron

Great hecatonicosafaceted prismatohecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ghif phix
Elements
Cells	600 tetrahedra, 720 pentagrammic prisms, 120 quasirhombicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagrams
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemipodium, edge lengths 1 (top triangle), (√5–1)/2 (base pseudo-triangle), and √2 (sides)
Measures (edge length 1)
Circumradius	$3-{\sqrt {5}}\approx 0.76393$
Dichoral angles	Qrid–4–stip: $\arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }$
	Qrid–3–tet: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
	Qrid–5/2–stip: 54°
Number of external pieces	171600
Level of complexity	652
Related polytopes
Army	Sidpixhi
Regiment	Gixhihy
Conjugate	Small hecatonicosafaceted prismatohecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	1200
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great hecatonicosafaceted prismatohecatonicosihexacosichoron, or ghif phix, is a nonconvex uniform polychoron that consists of 120 quasirhombicosidodecahedra, 600 tetrahedra, and 720 pentagrammic prisms. Three quasirhombicosidodecahedra, one tetrahedron, and three pentagrammic prisms join at each vertex.

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

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great hexacosihecatonicosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#501).