Small great dishecatonicosachoron

Small great dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sigady
Elements
Cells	120 small dodecicosahedra, 120 icosidodecatruncated icosidodecahedra
Faces	2400 hexagons, 1440 decagons, 720 decagrams
Edges	3600+7200
Vertices	3600
Vertex figure	Crossed butterfly wedge, edge lengths √3 (4), √(5+√5)/2 (4), and √(5–√5)/2 (2)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {15+3{\sqrt {5}}}{2}}}\approx 3.29456$
Dichoral angles	Siddy–10–idtid: 144°
	Siddy–6–idtid: 120°
	Idtid–10/3–idtid: 108°
Related polytopes
Army	Semi-uniform Srix, edge lengths ${\frac {3-{\sqrt {5}}}{2}}$ (icosidodecahedra), 1 (main triangles)
Regiment	Swavixady
Conjugate	Great great dishecatonicosachoron
Abstract & topological properties
Flag count	144000
Euler characteristic	–2880
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

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

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#260).