Small dodecicosahedral prism

Small dodecicosahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Siddipe
Elements
Cells	20 hexagonal prisms, 12 decagonal prisms, 2 small dodecicosahedra
Faces	60+60 squares, 40 hexagons, 24 decagons
Edges	60+120+120
Vertices	120
Vertex figure	Butterfly pyramid, edge lengths √3, √(5+√5)/2, √3, √(5+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {19+3{\sqrt {5}}}{8}}}\approx 1.79263$
Dichoral angles	Siddy–6–hip: 90°
	Siddy–10–dip: 90°
	Hip–4–dip #1: $\arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18768^{\circ }$
	Hip–4–dip #2: $\arccos \left({\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 37.37737^{\circ }$
Height	1
Number of external pieces	504
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Siidip
Dual	Small dodecicosacronic tegum
Conjugate	Great dodecicosahedral prism
Abstract & topological properties
Euler characteristic	–30
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small dodecicosahedral prism or siddipe is a prismatic uniform polychoron that consists of 2 small dodecicosahedra, 20 hexagonal prisms, and 12 decagonal prisms. Each vertex joins 1 small dodecicosahedron, 2 hexagonal prisms, and 2 decagonal prisms. As the name suggests, it is a prism based on the small dodecicosahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#943).