Small hecatonicosafaceted hecatonicosihexacosihecatonicosachoron

Small hecatonicosafaceted hecatonicosihexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Shi fohixhi
Elements
Cells	600 tetrahedra, 120 truncated great dodecahedra, 120 small ditrigonal dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagrams, 1440 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemipodium, edge lengths 1 (top triangle), (√5–1)/2 (base pseudo-triangle), and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{11+3\sqrt5}{2}} \approx 2.97558$
Dichoral angles	Sidditdid–10–tigid: 144°
	Sidditdid–3–tet: $\arccos\left(-\frac{\sqrt{10}}{4}\right) ≈ 142.23876°$
	Sidditdid–5/2–tigid: 72°
Number of external pieces	90120
Level of complexity	193
Related polytopes
Army	Semi-uniform Sidpixhi
Regiment	Shihix
Conjugate	Great hecatonicosafaceted hecatonicosihexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	–360
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small hecatonicosafaceted hecatonicosihexacosihecatonicosachoron, or shi fohixhi, is a nonconvex uniform polychoron that consists of 120 small ditrigonal dodecicosidodecahedra, 600 tetrahedra, and 120 truncated great dodecahedra. Three small ditrigonal dodecicosidodecahedra, one tetrahedron, and three truncated great dodecahedra join at each vertex.

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

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#508).