Small tritrigonary dishexacosidishecatonicosachoron

Small tritrigonary dishexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stut dixady
Coxeter diagram	x3x3o3o5*a3/2*c )
Elements
Cells	600 tetrahedra, 600 octahemioctahedra, 120 great ditrigonary icosidodecahedra, 120 truncated icosahedra
Faces	2400+2400 triangles, 1440 pentagons, 2400 hexagons
Edges	3600+7200
Vertices	2400
Vertex figure	Crossed retrotriangular cupola, edge lengths 1 (top triangle and 3 edges of base tripod), (1+√5)/2 (remaining base edges), and √3 (side edges)
Measures (edge length 1)
Circumradius	${\sqrt {8+3{\sqrt {5}}}}\approx 3.83513$
Hypervolume	$5{\frac {815+358{\sqrt {5}}}{4}}\approx 2019.39042$
Dichoral angles	Tet–3–oho: $\arccos \left(-{\frac {1+3{\sqrt {5}}}{8}}\right)\approx 164.47751^{\circ }$
	Gidtid–3–oho: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Oho–6–ti: $\arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.76124^{\circ }$
	Gidtid–5–ti: 36°
Related polytopes
Army	Semi-uniform sidpixhi, edge lengths ${\frac {{\sqrt {5}}-1}{2}}$ (dodecahedra), 1 (tetrahedra)
Regiment	Stut phiddix
Conjugate	Great tritrigonary dishexacosidishecatonicosachoron
Abstract & topological properties
Flag count	144000
Euler characteristic	–1200
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small tritrigonary dishexacosidishecatonicosachoron, or stut dixady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 truncated icosahedra, 600 octahemioctahedra, and 120 great ditrigonary icosidodecahedra. 1 tetrahedron, 3 truncated icosahedra, 3 octahemioctahedra, and 1 great ditrigonary icosidodecahedron join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small tritrigonary prismatohecatonicosidishexacosichoron.

External links

• Bowers, Jonathan. "Category 24: Stut Phiddix Regiment" (#1312).

• Klitzing, Richard. "stut dixady".