Great hecatonicosafaceted hecatonicosihexacosihecatonicosachoron

Great hecatonicosafaceted hecatonicosihexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gohi fohixhi
Elements
Cells	600 tetrahedra, 120 quasitruncated small stellated dodecahedra, 120 great ditrigonal dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagons, 1440 pentagrams
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemiantipodium, edge lengths 1 (top triangle), (1+√5)/2 (base pseudo-triangle), and √(5–√5)/2 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{11-3\sqrt5}{2}} \approx 1.46489$
Dichoral angles	Gidditdid–10/3–quit sissid: 72°
	Gidditdid–3–tet: $\arccos\left(\frac{\sqrt{10}}{4}\right) ≈ 37.76124°$
	Gidditdid–5–quit sissid: 90°
Number of external pieces	126600
Level of complexity	349
Related polytopes
Army	Semi-uniform Sidpixhi
Regiment	Gixhidy
Conjugate	Small hecatonicosafaceted hecatonicosihexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	–360
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great hecatonicosafaceted hecatonicosihexacosihecatonicosachoron, or gohi fohixhi, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 120 quasitruncated small stellated dodecahedra, and 120 great ditrigonal dodecicosidodecahedra. One tetrahedron, three quasitruncated small stellated dodecahedra, and three great ditrigonal dodecicosidodecahedra join at each vertex.

It also has 120 quasitruncated great stellated dodecahedra and 120 dodecahedra as pseudofacets.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#476).