Great ditrigonary hexacosihecatonicosachoron

Great ditrigonary hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidtixhi
Coxeter diagram	x3o3o3/2o5*b ()
Elements
Cells	600 tetrahedra, 120 icosahedra
Faces	2400 triangles
Edges	1200
Vertices	120
Vertex figure	Great ditrigonary icosidodecahedron, edge length 1
Edge figure	(tet 3 ike 3)×3
Measures (edge length 1)
Circumradius	1
Hypervolume	$25\frac{1+2\sqrt5}{4} ≈ 34.20085$
Dichoral angle	$\arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 97.76124^\circ$
Central density	39
Number of external pieces	57600
Level of complexity	154
Related polytopes
Army	Ex
Regiment	Sishi
Company	Sidtixhi
Dual	Great triambic icosahedral hecatonicosachoron
Conjugate	Small ditrigonary hexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great ditrigonary hexacosihecatonicosachoron, or gidtixhi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 regular icosahedra. 12 icosahedra and 20 tetrahedra join at each vertex, with a great ditrigonary icosidodecahedron as the vertex figure.

It has the same set of triangular faces as the small ditrigonary hexacosihecatonicosachoron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 17: Sishi Regiment" (#766).

• Klitzing, Richard. "gidtixhi".