Icosidodecatruncated icosidodecahedral prism

Icosidodecatruncated icosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Idtiddip
Coxeter diagram	x x5/3x3x5*b ()
Elements
Cells	20 hexagonal prisms, 12 decagonal prisms, 12 decagrammic prisms, 2 icosidodecatruncated icosidodecahedra
Faces	60+60+60 squares, 40 hexagons, 24 decagons, 24 decagrams
Edges	120+120+120+120
Vertices	240
Vertex figure	Irregular tetrahedron, edge lengths √3, √(5+√5)/2, √(5–√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{17}}{2} ≈ 2.06155$
Hypervolume	80
Dichoral angles	Hip–4–stiddip: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263^\circ$
	Dip–4–stiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ$
	Hip–4–dip: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232^\circ$
	Idtid–10/3–stiddip: 90°
	Idtid–10–dip: 90°
	Idtid–6–hip: 90°
Height	1
Central density	4
Number of pieces	154
Related polytopes
Army	Semi-uniform Griddip
Regiment	Idtiddip
Dual	Tridyakis icosahedral tegum
Conjugate	Icosidodecatruncated icosidodecahedral prism
Abstract properties
Euler characteristic	–18
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The icosidodecatruncated icosidodecahedral prism or idtiddip, is a prismatic uniform polychoron that consists of 2 icosidodecatruncated icosidodecahedra, 12 decagrammic prisms, 12 decagonal prisms, and 20 hexagonal prisms. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the icosidodecatruncated icosidodecahedron.

Vertex coordinates

The vertices of an icosidodecatruncated icosidodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$
• $\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac12\right),$
• $\left(±1,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±\frac12\right),$
• $\left(±\frac32,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12\right),$
• $\left(±\frac12,\,±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#950).

• Klitzing, Richard. "idtiddip".