Small hexacosifaceted trishecatonicosachoron

Small hexacosifaceted trishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Saxifthi
Elements
Cells	120 great stellated dodecahedra, 120 truncated dodecahedra, 120 small ditrigonal dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagrams, 1440 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemipodium, edge lengths (√5–1)/2 (top triangle), 1 (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–5/2–gissid: 144°
	Sidditdid–10–tid: 108°
	Sidditdid–3–tid: 60°
Number of external pieces	82200
Level of complexity	341
Related polytopes
Army	Semi-uniform Sidpixhi
Regiment	Shihix
Conjugate	Great hexacosifaceted trishecatonicosachoron
Abstract & topological properties
Euler characteristic	120
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small hexacosifaceted trishecatonicosachoron, or saxifthi, is a nonconvex uniform polychoron that consists of 120 small ditrigonal dodecicosidodecahedra, 120 great stellated dodecahedra, and 120 truncated dodecahedra. Three small ditrigonal dodecicosidodecahedra, one great stellated dodecahedron, and three truncated dodecahedra join at each vertex.

It also has 600 tetrahedra and 120 truncated great 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" (#509).