Small ditrigonal dodecicosidodecahedral prism

Small ditrigonal dodecicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sidditdiddip
Coxeter diagram	x x5/3o3x5*b ()
Elements
Cells	20 triangular prisms, 12 pentagrammic prisms, 12 decagonal prisms, 2 small ditrigonal dodecicosidodecahedra
Faces	40 triangles, 60+60 squares, 24 pentagrams, 24 decagons
Edges	60+120+120
Vertices	120
Vertex figure	Crossed isosceles trapezoidal pyramid, edge lengths 1, √(5+√5)/2, (√5–1)/2, √(5+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{19+3\sqrt5}{8}} ≈ 1.79263$
Hypervolume	$7\frac{15+\sqrt5}{6} ≈ 20.10875$
Dichoral angles	Trip–4–stiddip: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232°$
	Sidditdid–5/2–stip: 90°
	Sidditdid–3–trip: 90°
	Sidditdid–10–dip: 90°
	Stip–4–dip: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495°$
Height	1
Central density	4
Number of pieces	238
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Siidip
Dual	Small ditrigonal dodecacronic hexecontahedral tegum
Conjugate	Great ditrigonal dodecicosidodecahedral prism
Abstract properties
Euler characteristic	–18
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

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

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#942).

• Klitzing, Richard. "sidditdiddip".