Great dirhombicosidodecahedral prism

Great dirhombicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidriddip
Coxeter diagram	x2s3s5/2s3/2s5/3*bØ*d *cØ*e
Elements
Cells	40 triangular prisms, 60 cubes, 24 pentagrammic prisms, 2 great dirhombicosidodecahedra
Faces	80 triangles, 120+120+120 squares, 48 pentagrams
Edges	60+240+240
Vertices	120
Vertex figure	Irregular octagonal pyramid, edge lengths 1, √2, (√5–1)/2, √2, 1, √2, (√5–1)/2, √2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt3}{2} ≈ 0.86603$
Hypervolume	0
Dichoral angles	Gidrid–5/2–stip: 90°
	Gidrid–3–trip: 90°
	Gidrid–4–cube: 90°
	Stip–4–cube: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{5}}\right) ≈ 71.03929^\circ$
	Trip–4–cube: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$
Height	1
Central density	0
Number of pieces	1282
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Gidriddip
Dual	Great dirhombicosidodecacronic tegum
Abstract properties
Euler characteristic	–58
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The great dirhombicosidodecahedral prism or gidriddip is a prismatic uniform polychoron that consists of 2 great dirhombicosidodecahedra, 24 pentagrammic prisms, 40 triangular prisms, and 60 cubes (the latter three of these form pairs in the same hyperplane). Each vertex joins 1 great dirhombicosidodecahedron, 2 pentagrammic prisms, 2 triangular prisms, and 4 cubes. As the name suggests, it is a prism based on the great dirhombicosidodecahedron.

Vertex coordinates

A great dirhombicosidodecahedral prism of edge length 1 has vertex coordinates given by all even permutations of the first three coordinates of:

• $\left(±\sqrt{\frac{\sqrt5-1-2\sqrt{\sqrt5-2}}{8}},\,±\sqrt{\frac{3-\sqrt5-\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2+\sqrt{2\sqrt5-2}}{8}},\,±\frac12\right),$
• $\left(0,\,±\frac{\sqrt{3-\sqrt5}}{2},\,±\frac{\sqrt{\sqrt5-1}}{2},\,±\frac12\right),$
• $\left(±\sqrt{\frac{3-\sqrt5+\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2-\sqrt{2\sqrt5-2}}{8}},\,±\sqrt{\frac{\sqrt5-1+2\sqrt{\sqrt5-2}}{8}},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#962).

• Klitzing, Richard. "gidriddip".