Small hecatonicosafaceted hexacosidishecatonicosachoron

Small hecatonicosafaceted hexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Shi fixady
Elements
Cells	600 tetrahedra, 120 truncated great icosahedra, 120 small icosicosidodecahedra
Faces	2400 triangles, 1440 pentagrams, 2400 hexagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemiantipodium, edge lengths 1 (top triangle), (√5–1)/2 (base pseudo-triangle), and √3 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{13-3\sqrt5}{2}} \approx 1.77367$
Dichoral angles	Siid–6–tiggy: 120°
	Siid–3–tet: $\arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 97.76124°$
	Siid–5/2–tiggy: 72°
Number of external pieces	299040
Level of complexity	955
Related polytopes
Army	Semi-uniform Sidpixhi
Regiment	Sadixady
Conjugate	Great hecatonicosafaceted hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic	600
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small hecatonicosafaceted hexacosidishecatonicosachoron, or shi fixady, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 120 truncated great icosahedra, and 120 small icosicosidodecahedra. One tetrahedron, three truncated great icosahedra, and three small icosicosidodecahedra join at each vertex.

It also has 120 great stellated dodecahedra and 600 truncated tetrahedra as pseudofacets.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#470).