Small dishecatonicosachoron

Small dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sidahi
Elements
Cells	120 small dodecicosahedra, 120 great rhombicosidodecahedra
Faces	1800 squares, 2400 hexagons, 1440 decagons
Edges	3600+7200
Vertices	3600
Vertex figure	Crossed butterfly wedge, edge lengths √2 (2), √3 (4), and √(5+√5)/2 (4)
Measures (edge length 1)
Circumradius	${\sqrt {15+6{\sqrt {5}}}}\approx 5.33070$
Dichoral angles	Siddy–10–grid: 144°
	Siddy–6–grid: 120°
	Grid-4–grid: 90°
Related polytopes
Army	Semi-uniform Srahi, edge lengths ${\frac {{\sqrt {5}}-1}{2}}$ (pentagons), 1 (octahedra)
Regiment	Wavhiddix
Conjugate	Great dishecatonicosachoron
Abstract & topological properties
Flag count	144000
Euler characteristic	–1800
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small dishecatonicosachoron, or sidahi, is a nonconvex uniform polychoron that consists of 120 small dodecicosahedra and 120 great rhombicosidodecahedra. Two small dodecicosahedra and four great rhombicosidodecahedra join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the sphenoverted hecatonicosidishexacosichoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#246).