Small ditrigonary hexacosihecatonicosachoron

Small ditrigonary hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sidtixhi
Coxeter diagram	x3o3o3o5/2*b ()
Elements
Cells	600 tetrahedra, 120 great icosahedra
Faces	2400 triangles
Edges	1200
Vertices	120
Vertex figure	Small ditrigonary icosidodecahedron, edge length 1
Edge figure	(tet 3 gike 3)×3
Measures (edge length 1)
Circumradius	1
Hypervolume	$25{\frac {2{\sqrt {5}}-1}{4}}\approx 21.70085$
Dichoral angle	$\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
Central density	9
Number of external pieces	15840
Level of complexity	51
Related polytopes
Army	Ex, edge length ${\frac {{\sqrt {5}}-1}{2}}$
Regiment	Sishi
Company	Sidtixhi
Dual	Small triambic icosahedral hecatonicosachoron
Conjugate	Great ditrigonary hexacosihecatonicosachoron
Convex core	Truncated hexacosichoron
Abstract & topological properties
Flag count	28800
Euler characteristic	600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

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

Vertex coordinates

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

Related polychora

The small ditrigonary hexacosihecatonicosachoron has the same edges as the regular small stellated hecatonicosachoron. It shares its face arrangement with the ditrigonary dishecatonicosachoron and the great ditrigonary hexacosihecatonicosachoron. Also sharing this set of faces is the dodecahedronary hexacosichoron, a uniform compound of 25 icositetrachora. Besides these three polychora, there is only one other face-transitive uniform polychoron which is not regular, namely the tesseractihemioctachoron.

External links

• Bowers, Jonathan. "Category 17: Sishi Regiment" (#764).

• Klitzing, Richard. "sidtixhi".