Small prismatohexacosidishecatonicosachoron

Small prismatohexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Spixady
Coxeter diagram	x3x3/2o5x5*b ()
Elements
Cells	720 pentagonal prisms, 600 truncated tetrahedra, 120 small dodecicosidodecahedra, 120 great rhombicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagons, 2400 hexagons, 1440 decagons
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Crossed isosceles trapezoidal pyramid, base edge lengths 1, √(5+√5)/2, (1+√5)/2, √(5+√5)/2; lateral edge lengths √2, √2, √3, √3
Measures (edge length 1)
Circumradius	${\frac {5{\sqrt {2}}+3{\sqrt {10}}}{2}}\approx 8.27895$
Hypervolume	$25{\frac {4594+2101{\sqrt {5}}}{4}}\approx 58074.8676$
Dichoral angles	Saddid–5–pip: 162°
	Saddid–3–tut: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Grid–4–pip: $\arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }$
	Saddid–10–grid: 144°
	Tut–6–grid: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
Related polytopes
Army	Prahi
Regiment	Prahi
Conjugate	Great prismatohexacosidishecatonicosachoron
Abstract & topological properties
Flag count	230400
Euler characteristic	–1080
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small prismatohexacosidishecatonicosachoron, or spixady, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 600 truncated tetrahedra, 120 small dodecicosidodecahedra, and 120 great rhombicosidodecahedra. 1 pentagonal prism, 1 truncated tetrahedron, 1 small dodecicosidodecahedron, and 2 great rhombicosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#365).

• Klitzing, Richard. "spixady".