Great hexacosifaceted hexacosidishecatonicosachoron

Great hexacosifaceted hexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gix fixady
Elements
Cells	600 truncated tetrahedra, 120 dodecahedra, 120 great icosicosidodecahedra
Faces	2400 triangles, 1440 pentagons, 2400 hexagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemipodium, edge lengths (1+√5)/2 (top triangle), 1 (base pseudo-triangle), and √3 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{13+3\sqrt5}{2}} \approx 3.13912$
Dichoral angles	Giid–5–doe: 144°
	Giid–3–tut: $\arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 97.76124°$
	Giid–6–tut: $\arccos\left(\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 22.23876°$
Number of external pieces	107160
Level of complexity	349
Related polytopes
Army	Thi
Regiment	Gidthixhi
Conjugate	Small hexacosifaceted hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic	600
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

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

It also has 120 truncated icosahedra and 600 tetrahedra as pseudofacets.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#494).