Small dishecatonicosacoincidic hecatonicosachoron

Small dishecatonicosacoincidic hecatonicosachoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sid hichi
Elements
Cells	120 icosahedra 120 great dodecahedra 120 small rhombicosidodecahedra
Faces	2400 triangles 1800 squares 1440 pentagons
Edges	3600
Vertices	720
Vertex figure	Faceting of pentagonal prism
Edge figure	ike.srid.srid.gad.srid.srid
Measures (edge length 1)
Circumradius	${\sqrt {5+2{\sqrt {5}}}}\approx 3.07768$
Hypervolume	$\approx 2578.82926$
Related polytopes
Army	Rox
Regiment	Rox
Conjugate	Grand retroinverted dishecatonicosacoincidic hecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Exotic

The small dishecatonicosacoincidic hecatonicosachoron is an ECC uniform polychoron that consists of 120 icosahedra, 120 great dodecahedra, and 120 small rhombicosidodecahedra. 2 icosahedra, 2 great dodecahedra, and 10 small rhombicosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified hexacosichoron.