Rhombic small hexacosihecatonicosachoron

Rhombic small hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Rassixhi
Elements
Cells	720 pentagonal prisms 600 cubohemioctahedra 120 truncated icosahedra
Faces	3600 squares 1440 pentagons 2400 hexagons
Edges	3600+7200
Vertices	3600
Vertex figure	Butterfly wedge, edge lengths (1+√5)/2 (bases), √2 (sides of outer triangles), and √3 (sides of inner triangles)
Measures (edge length 1)
Circumradius	${\sqrt {19+8{\sqrt {5}}}}\approx 6.07359$
Dichoral angles	Cho–4–pip: $\arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}}{10}}}\right)\approx 166.71747^{\circ }$
	Ti–5–pip: 162°
	Cho–6–ti: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
Related polytopes
Army	Srix
Regiment	Srix
Conjugate	Rhombic great hexacosihecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	144000
Euler characteristic	–1200
Orientable	No
Properties
Symmetry	H4, order 14400
Flag orbits	10
Convex	No
Nature	Tame

The rhombic small hexacosihecatonicosachoron, or rassixhi, is a nonconvex uniform polychoron that consists of 120 truncated icosahedra, 600 cubohemioctahedra, and 720 pentagonal prisms. 2 of each type of cell join at each vertex.

Vertex coordinates

The vertices are the same as those of the small rhombated hexacosichoron, its regiment colonel.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#167).