Icosidodecadodecahedral prism

The icosidodecadodecahedral prism or ididdip is a prismatic uniform polychoron that consists of 2 icosidodecadodecahedra, 12 pentagonal prisms, 12 pentagrammic prisms, and 20 hexagonal prisms. Each vertex joins 1 icosidodecadodecahedron, 1 pentagonal prism, 1 pentagrammic prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the icosidodecadodecahedron.

Icosidodecadodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Ididdip
Coxeter diagram	x o5/3x3x5*b ()
Elements
Cells	12 pentagonal prisms, 12 pentagrammic prisms, 20 hexagonal prisms, 2 icosidodecadodecahedra
Faces	60+60 squares, 24 pentagons, 24 pentagrams, 40 hexagons
Edges	60+120+120
Vertices	120
Vertex figure	Crossed isosceles trapezoidal pyramid, edge lengths (√5–1)/2, √3, (1+√5)/2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt2 ≈ 1.41421$
Hypervolume	20
Dichoral angles	Pip–4–hip: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232^\circ$
	Ided–5/2–stip: 90°
	Ided–5–pip: 90°
	Ided–6–hip: 90°
	Stip–4–hip: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ$
Height	1
Central density	4
Number of external pieces	434
Related polytopes
Army	Semi-uniform Tipe
Regiment	Radiddip
Dual	Medial icosacronic hexecontahedral tegum
Conjugate	Icosidodecadodecahedral prism
Abstract & topological properties
Euler characteristic	–18
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#930).

• Klitzing, Richard. "ididdip".