Great tritrigonary trishecatonicosihexacosichoron

Great tritrigonary trishecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Getit thix
Coxeter diagram	(x3x3/2o3o5/3*a5*c)
Elements
Cells	600 tetrahedra, 120 ditrigonary dodecadodecahedra, 120 truncated great icosahedra, 120 great icosicosidodecahedra
Faces	2400 triangles, 1440 pentagons, 1440 pentagrams, 2400 hexagons
Edges	3600+7200
Vertices	2400
Vertex figure	Crossed retrotriangular cupola, edge lengths 1 (top triangle), (1+√5)/2 (3 edges of base tripod), (√5–1)/2 (remaining base edges), and √3 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {8-3{\sqrt {5}}}}\approx 1.13657$
Hypervolume	$5{\frac {841{\sqrt {5}}-1280}{4}}\approx 750.66646$
Dichoral angles	Ditdid–5–giid: 108°
	Tet–3–giid: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
	Ditdid–5/2–tiggy: 72°
	Giid–6–tiggy: 60°
Related polytopes
Army	Semi-uniform sidpixhi
Regiment	Getit xethi
Conjugate	Small tritrigonary trishecatonicosihexacosichoron
Abstract & topological properties
Euler characteristic	–1680
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great tritrigonary trishecatonicosihexacosichoron, or getit thix, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 truncated great icosahedra, 120 great icosicosidodecahedra, and 120 ditrigonary dodecadodecahedra. 1 tetrahedron, 3 truncated great icosahedra, 3 great icosicosidodecahedra, and 1 ditrigonary dodecadodecahedron join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great tritrigonary hexacositrishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 25: Getit Xethi Regiment" (#1388).

• Klitzing, Richard. "getit thix".