Small dishecatonicosintercepted dishecatonicosachoron

Small dishecatonicosintercepted dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sid hinady
Elements
Cells	120 dodecadodecahedra, 120 truncated great dodecahedra, 120 small rhombicosidodecahedra, 120 great rhombicosidodecahedra
Faces	1200 triangles, 3600 squares, 1440 pentagons, 1440 pentagrams, 1200 hexagons, 1440 decagons
Edges	3600+7200
Vertices	3600
Vertex figure	Inverted wedge, edge lengths 1 (1), √2 (4), (1+√5)/2 (2), (√5–1)/2 (2), √3 (2), and √(5+√5)/2 (4)
Measures (edge length 1)
Circumradius	${\sqrt {10+4{\sqrt {5}}}}\approx 4.35250$
Hypervolume	$5{\frac {8885+3981{\sqrt {5}}}{4}}\approx 22233.4833$
Dichoral angles	Srid–5–did: 144°
	Srid–3–srid: 120°
	Did–5/2–tigid: 108°
	Tigid–10–grid: 108°
	Srid–4–grid: 90°
	Grid–6–grid: 60°
Related polytopes
Army	Semi-uniform Srix, edge lengths ${\frac {{\sqrt {5}}-1}{2}}$ (icosidodecahedra), 1 (main triangles)
Regiment	Sirfix
Conjugate	Grand hecatonicosintercepted trishecatonicosachoron
Abstract & topological properties
Flag count	216000
Euler characteristic	2640
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small dishecatonicosintercepted dishecatonicosachoron, or sid hinady, is a nonconvex uniform polychoron that consists of 120 dodecadodecahedra, 120 small rhombicosidodecahedra, 120 truncated great dodecahedra, and 120 great rhombicosidodecahedra. One dodecadodecahedron, two small rhombicosidodecahedra, two truncated great dodecahedra, and four great rhombicosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#177).