Icosidodecatruncated icosidodecahedral prism

Icosidodecatruncated icosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
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	${\frac {\sqrt {17}}{2}}\approx 2.06155$
Hypervolume	80
Dichoral angles	Hip–4–stiddip: $\arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 142.62263^{\circ }$
	Dip–4–stiddip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Hip–4–dip: $\arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }$
	Idtid–10/3–stiddip: 90°
	Idtid–10–dip: 90°
	Idtid–6–hip: 90°
Height	1
Central density	4
Number of external pieces	154
Related polytopes
Army	Semi-uniform Griddip
Regiment	Idtiddip
Dual	Tridyakis icosahedral tegum
Conjugate	Icosidodecatruncated icosidodecahedral prism
Abstract & topological properties
Euler characteristic	–18
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:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm 1,\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {3}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {3{\sqrt {5}}-1}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right).$

External links

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

• Klitzing, Richard. "idtiddip".