Small ditetrahedrofissary dishecatonicosachoron

Small ditetrahedrofissary dishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sadtifady
Coxeter diagram	(x3/2o5x3/2o5*a5*c)/2
Elements
Cells	120 icosidodecahedra, 120 small dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagons, 720 decagons
Edges	3600
Vertices	600
Vertex figure	Compound of 3 crossed rectangular trapezoprisms, edge lengths 1 and (1+√5)/2 (base) and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Hypervolume	$5(25+3\sqrt5) ≈ 158.54102$
Dichoral angles	Saddid–10–saddid: 144º
	Id–3–saddid: 60º
	Id–5–saddid: 36º
Related polytopes
Army	Hi
Regiment	Sidtaxhi
Conjugate	Great ditetrahedrofissary dishecatonicosachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small ditetrahedrofissary dishecatonicosachoron, or sadtifady, is a nonconvex fissary uniform polychoron that consists of 120 icosidodecahedra and 120 small dodecicosidodecahedra. 6 icosidodecahedra and 12 small dodecicosidodecahedra join at each vertex.

It is fissary with vertices coinciding by 3, and edges coinciding by two.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#F14).

• Klitzing, Richard. "sadtifady".