Small hexacosifaceted hexacosidishecatonicosachoron

Small hexacosifaceted hexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Six fixady
Elements
Cells	600 truncated tetrahedra, 120 great stellated dodecahedra, 120 small icosicosidodecahedra
Faces	2400 triangles, 1440 pentagrams, 2400 hexagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemiantipodium, edge lengths (√5–1)/2 (top triangle), 1 (base pseudo-triangle), and √3 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{13-3\sqrt5}{2}} \approx 1.77367$
Dichoral angles	Siid–6–tut: $\arccos\left(\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 82.23876°$
	Siid–5/2–gissid: 72°
	Siid–3–tut: $\arccos\left(\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 22.23876°$
Number of external pieces	294120
Level of complexity	925
Related polytopes
Army	Semi-uniform Sidpixhi
Regiment	Sadixady
Conjugate	Great hexacosifaceted hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic	600
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small hexacosifaceted hexacosidishecatonicosachoron, or six fixady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 600 truncated tetrahedra, and 120 small icosicosidodecahedra. One great stellated dodecahedron, three truncated tetrahedra, and three small icosicosidodecahedra join at each vertex.

It also has 120 truncated great icosahedra and 600 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" (#469).