Great skewverted ditrigonal hexacositrishecatonicosachoron

Great skewverted ditrigonal hexacositrishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gikkiv datixathi
Coxeter diagram	x3x3o5/3x5/3*a3/2*c *b5*d
Elements
Cells	600 octahemioctahedra, 120 small ditrigonal dodecicosidodecahedra, 120 great dodecicosidodecahedra, 120 icosidodecatruncated icosidodecahedra
Faces	2400+2400 triangles, 1440 pentagrams, 2400 hexagons, 1440 decagons, 1440 decagrams
Edges	7200+7200+7200
Vertices	7200
Vertex figure	Crossed skewed wedge, base edge lengths 1, 1, (√5–1)/2; lateral edge lengths √3, √(5+√5)/2, √(5+√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {13-4{\sqrt {5}}}}\approx 2.03188$
Hypervolume	$5(893{\sqrt {5}}-1810)\approx 934.04352$
Dichoral angles	Gaddid–3–oho: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Gaddid–5/2–sidditdid: 108°
	Sidditdid–10–idtid: 108°
	Sidditdid–3–oho: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
	Oho–6–idtid: $\arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }$
	Gaddid–10/3–idtid: 72°
Related polytopes
Army	Semi-uniform Grix
Regiment	Gik vixathi
Conjugate	Small skewverted ditrigonal hexacositrishecatonicosachoron
Abstract & topological properties
Euler characteristic	–3840
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great skewverted ditrigonal hexacositrishecatonicosachoron, or gikkiv datixathi, is a nonconvex uniform polychoron that consists of 600 octahemioctahedra, 120 small ditrigonal dodecicosidodecahedra, 120 great dodecicosidodecahedra, and 120 icosidodecatruncated icosidodecahedra. 1 octahemioctahedron, 1 small ditrigonal dodecicosidodecahedron, 1 great dodecicosidodecahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great skewverted hexacositrishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 14: Skewverts" (#568).