Small dodecicosidodecahedral prism

Small dodecicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Saddiddip
Coxeter diagram	x x3/2o5x5*b ()
Elements
Cells	20 triangular prisms, 12 pentagonal prisms, 12 decagonal prisms, 2 small dodecicosidodecahedra
Faces	40 triangles, 60+60 squares, 24 pentagons, 24 decagons
Edges	60+120+120
Vertices	120
Vertex figure	Crossed isosceles trapezoidal pyramid, edge lengths 1, √(5+√5)/2, (1+√5)/2, √(5+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825$
Hypervolume	$2\frac{45+17\sqrt5}{3} ≈ 55.34210$
Dichoral angles	Pip–4–dip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Saddid–5–pip: 90°
	Saddid–3–trip: 90°
	Saddid–10–dip: 90°
	Trip–4–dip: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737°$
Height	1
Central density	2
Number of pieces	194
Related polytopes
Army	Sriddip
Regiment	Sriddip
Dual	Small dodecacronic hexecontahedral tegum
Conjugate	Great dodecicosidodecahedral prism
Abstract properties
Euler characteristic	–18
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small dodecicosidodecahedral prism or saddiddip is a prismatic uniform polychoron that consists of 2 small dodecicosidodecahedra, 12 pentagonal prisms, 20 triangular prisms, and 12 decagonal prisms. Each vertex joins 1 small dodecicosidodecahedron, 1 pentagonal prism, 1 triangular prism, and 2 decagonal prisms. As the name suggests, it is a prism based on the small dodecicosidodecahedron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small rhombicosidodecahedral prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#927).

• Klitzing, Richard. "saddiddip".