Small skewverted dishexacosidishecatonicosachoron

Small skewverted dishexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sik vadixady
Coxeter diagram	o3x3x3x5*a3/2*c ()
Elements
Cells	600 octahemioctahedra, 600 truncated octahedra, 120 small rhombicosidodecahedra, 120 great icosicosidodecahedra
Faces	2400+2400 triangles, 3600 squares, 1440 pentagons, 2400+2400 hexagons
Edges	7200+7200+7200
Vertices	7200
Vertex figure	Crossed skewed wedge, base edge lengths 1, 1, (1+√5)/2; lateral edge lengths √2, √3, √3
Measures (edge length 1)
Circumradius	${\sqrt {13+4{\sqrt {5}}}}\approx 4.68447$
Hypervolume	$65{\frac {265+77{\sqrt {5}}}{2}}\approx 14208.2601$
Dichoral angles	Giid–3–oho: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Giid–5–srid: 144°
	Srid–3–oho: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Srid–4–toe: 135°
	Giid–6–toe: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
	Oho–6–toe: $\arccos \left({\frac {1+3{\sqrt {5}}}{8}}\right)\approx 15.52249^{\circ }$
Related polytopes
Army	Semi-uniform Prix, edge lengths ${\frac {3-{\sqrt {5}}}{2}}$ (truncated dodecahedra), 1 (bases of triangular prisms)
Regiment	Skiv datapixady
Conjugate	Great skewverted dishexacosidishecatonicosachoron
Abstract & topological properties
Flag count	259200
Euler characteristic	–1200
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small skewverted dishexacosidishecatonicosachoron, or sik vadixady, is a nonconvex uniform polychoron that consists of 600 octahemioctahedra, 600 truncated octahedra, 120 small rhombicosidodecahedra, and 120 great icosicosidodecahedra. 1 octahemioctahedron, 1 small rhombicosidodecahedron, 1 great icosicosidodecahedron, and 2 truncated octahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small skewverted ditrigonal prismatohexacosidishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 14: Skewverts" (#600).

• Klitzing, Richard. "sik vadixady".