Quasitruncated great grand stellated hecatonicosachoron

Quasitruncated great grand stellated hecatonicosachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Quit gogishi
Coxeter diagram	x5/3x3o3o ()
Elements
Cells	600 tetrahedra, 120 quasitruncated great stellated dodecahedra
Faces	2400 triangles, 720 decagrams
Edges	1200+3600
Vertices	2400
Vertex figure	Triangular pyramid, edge lengths 1 (base) and √(5–√5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angle	Quit gissid–3–tet: ; Quit gissid–10/3–quit gissid: 72°
Central density	409
Number of external pieces	103200
Level of complexity	252
Related polytopes
Army	Semi-uniform Sidpixhi, edge lengths (dodecahedra), (tetrahedra)
Regiment	Quit gogishi
Conjugate	Truncated hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	57600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Flag orbits	4
Convex	No
Nature	Tame

The quasitruncated great grand stellated hecatonicosachoron, or quit gogishi, is a convex uniform polychoron that consists of 600 regular tetrahedra and 120 quasitruncated great stellated dodecahedra. 1 tetrahedron and three quasitruncated great stellated dodecahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the great grand stellated hecatonicosachoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a quasitruncated great grand stellated hecatonicosachoron of edge length 1 are given by all permutations of:

$\left(\pm {\frac {1}{2}},\,\pm {\frac {5-2{\sqrt {5}}}{2}},\,\pm {\frac {5-2{\sqrt {5}}}{2}},\,\pm {\frac {5-2{\sqrt {5}}}{2}}\right)$ ,
$\left(\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {8-3{\sqrt {5}}}{2}}\right)$ ,
$\left(\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{2}}\right)$ ,

along with all even permutations of:

$\left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {13-5{\sqrt {5}}}{4}},\,\pm {\frac {5{\sqrt {5}}-11}{4}}\right)$ ,
$\left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {7{\sqrt {5}}-15}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{4}}\right)$ ,
$\left(0,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {5{\sqrt {5}}-9}{4}}\right)$ ,
$\left(0,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {8-3{\sqrt {5}}}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{4}}\right)$ ,
$\left(0,\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{2}},\,\pm ({\sqrt {5}}-2)\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {7{\sqrt {5}}-15}{4}},\,\pm {\frac {3-{\sqrt {5}}}{2}}\right)$ ,
$\left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {5-2{\sqrt {5}}}{2}}\right)$ ,
$\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {7{\sqrt {5}}-15}{4}},\,\pm {\frac {{\sqrt {5}}-2}{2}}\right)$ ,
$\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {13-5{\sqrt {5}}}{4}},\,\pm {\frac {5-2{\sqrt {5}}}{2}}\right)$ ,
$\left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm ({\sqrt {5}}-2),\,\pm {\frac {5{\sqrt {5}}-9}{4}},\,\pm {\frac {5-2{\sqrt {5}}}{2}}\right)$ ,
$\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {5{\sqrt {5}}-11}{4}},\,\pm {\frac {5-2{\sqrt {5}}}{2}}\right)$ ,
$\left(\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {5{\sqrt {5}}-11}{4}},\,\pm {\frac {5{\sqrt {5}}-9}{4}}\right)$ ,
$\left(\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {13-5{\sqrt {5}}}{4}},\,\pm ({\sqrt {5}}-2)\right)$ ,
$\left(\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{4}}\right)$ .