Quasirhombicosidodecahedral prism

The quasirhombicosidodecahedral prism or qriddip is a prismatic uniform polychoron that consists of 2 quasirhombicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 30 cubes. Each vertex joins 1 quasirhombicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 cubes. As the name suggests, it is a prism based on the quasirhombicosidodecahedron.

Quasirhombicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Qriddip
Coxeter diagram	x x5/3o3x ()
Elements
Cells	20 triangular prisms, 30 cubes, 12 pentagrammic prisms, 2 quasirhombicosidodecahedra
Faces	40 triangles, 60+60+60 squares, 24 pentagrams
Edges	60+120+120
Vertices	120
Vertex figure	Crossed trapezoidal pyramid, edge lengths 1, √2, (√5–1)/2, √2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403$
Hypervolume	$\frac{29\sqrt5-60}{3} ≈ 1.61532$
Dichoral angles	Qrid–5/2–stip: 90°
	Qrid–3–trip: 90°
	Qrid–4–cube: 90°
	Trip–4–cube: $\arccos\left(\frac{\sqrt{15}-\sqrt3}{6}\right) ≈ 69.09484°$
	Cube–4–stip: $\arccos\left(\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 58.28253°$
Height	1
Central density	13
Related polytopes
Army	Semi-uniform Tipe
Regiment	Gaddiddip
Dual	Great deltoidal hexecontahedral tegum
Conjugate	Small rhombicosidodecahedral prism
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame
Discovered by	{{{discoverer}}}

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#939).

• Klitzing, Richard. "qriddip".