Great tritrigonary hexacositrishecatonicosachoron

Great tritrigonary hexacositrishecatonicosachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Getit xethi
Coxeter diagram	x3o3o3x5/3a5/2c ()
Elements
Cells	600 tetrahedra, 120 small ditrigonary icosidodecahedra, 120 quasitruncated great stellated dodecahedra, 120 great dodecicosidodecahedra
Faces	2400+2400 triangles, 1440 pentagrams, 1440 decagrams
Edges	3600+7200
Vertices	2400
Vertex figure	Triangular cupola, edge lengths 1 (top triangle and 3 edges of base ditrigon), (√5–1)/2 (remaining base edfges), and √(5–√5)/2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Quit gissid–10/3–gaddid: 144°
	Tet–3–gaddid:
	Sidtid–3–gaddid: 120°
	Sidtid–5/2–gaddid: 108°
Number of external pieces	43200
Related polytopes
Army	Semi-uniform sidpixhi, edge lengths (dodecahedra), (tetrahedra)
Regiment	Getit xethi
Conjugate	Small tritrigonary hexacositrishecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	144000
Euler characteristic	–1680
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great tritrigonary hexacositrishecatonicosachoron, or getit xethi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 quasitruncated great stellated dodecahedra, 120 great dodecicosidodecahedra, and 120 small ditrigonary icosidodecahedra. 1 tetrahedron, 3 quasitruncated great stellated dodecahedra, 3 great dodecicosidodecahedra, and 1 small ditrigonary icosidodecahedron join at each vertex.

The great tritrigonary hexacositrishecatonicosachoron contains the vertices of an inscribed great quasitruncated icosidodecahedral prism.

Vertex coordinates[edit | edit source]

The vertices of a great tritrigonary hexacositrishecatonicosachoron of edge length 1 are all permutations of:

$\left(0,\,\pm 1,\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2{\sqrt {5}}-3}{2}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {4-{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {\sqrt {5}}{2}}\right),$

along with the even permutations of:

$\left(0,\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {2{\sqrt {5}}-3}{2}}\right),$
$\left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}}\right),$
$\left(0,\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {7-3{\sqrt {5}}}{4}}\right),$
$\left(0,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {4-{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}}\right),$
$\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{4}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm 1,\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {{\sqrt {5}}-2}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}}\right),$
$\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}}\right).$