Small dipentary trishecatonicosachoron

Small dipentary trishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sidipthi
Coxeter diagram	o5/2o3/2x5x5*b ()
Elements
Cells	120 great icosahedra, 120 great dodecahedra, 120 small dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagons, 720 decagons
Edges	3600+3600
Vertices	1440
Vertex figure	Crossed pentagrammic frustum, edge lengths 1 (small base), (1+√5)/2 (large base), and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {4+{\sqrt {5}}}}\approx 2.49721$
Hypervolume	$5{\frac {370+207{\sqrt {5}}}{2}}\approx 2082.16518$
Dichoral angles	Saddid–10–saddid: 72°
	Saddid–3–gike: 60°
	Saddid–5–gad: 36°
Related polytopes
Army	Semi-uniform Tex, edge lengths ${\frac {{\sqrt {5}}-1}{2}}$ (icosahedra), ${\frac {3-{\sqrt {5}}}{2}}$ (surrounded by truncated tetrahedra)
Regiment	Padohi
Conjugate	Great dipentary trishecatonicosachoron
Abstract & topological properties
Flag count	86400
Euler characteristic	–1560
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small dipentary trishecatonicosachoron, or sidipthi, is a nonconvex uniform polychoron that consists of 120 great icosahedra, 120 great dodecahedra, and 120 small dodecicosidodecahedra. 1 great icosahedron, 1 great dodecahedron, and 5 small dodecicosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 21: Padohi Regiment" (#988).

• Klitzing, Richard. "sidipthi".