Small retrotrishecatonicosachoron

Small retrotrishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sirthi
Elements
Cells	120 truncated icosahedra, 120 quasitruncated small stellated dodecahedra, 120 icosidodecatruncated icosidodecahedra
Faces	1440 pentagons, 2400 hexagons, 720 decagons, 1440 decagrams
Edges	3600+7200
Vertices	3600
Vertex figure	Isosceles triangular retroprism, edge lengths (1+√5)/2 (2), √3 (4), √(5+√5)/2 (4), and √(5–√5)/2 (2)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {11+{\sqrt {5}}}{2}}}\approx 2.57255$
Hypervolume	$15{\frac {180+199{\sqrt {5}}-}{2}}\approx 4687.33146$
Dichoral angles	Idtid–10–idtid: 108°
	Ti–5–quit sissid: 72°
	Idtid–6–ti: 60°
	Idtid–10/3–quit sissid: 36°
Related polytopes
Army	Srahi
Regiment	Swav ditathi
Conjugate	Great retrotrishecatonicosachoron
Abstract & topological properties
Euler characteristic	–1560
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small retrotrishecatonicosachoron, or sirthi, is a nonconvex uniform polychoron that consists of 120 quasitruncated small stellated dodecahedra, 120 truncated icosahedra, and 120 icosidodecatruncated icosidodecahedra. Two quasitruncated small stellated dodecahedra, two truncated icosahedra, and four icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#238).