Great icosidodecahedral prism

Great icosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Giddip
Coxeter diagram	x o5/2x3o ()
Elements
Cells	20 triangular prisms, 12 pentagrammic prisms, 2 great icosidodecahedra
Faces	40 triangles, 60 squares, 24 pentagrams
Edges	30+120
Vertices	60
Vertex figure	Rectangular pyramid, edge lengths 1, (√5–1)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {7-2{\sqrt {5}}}}{2}}\approx 0.79496$
Hypervolume	${\frac {45-17{\sqrt {5}}}{6}}\approx 1.16447$
Dichoral angles	Trip–4–stip: $\arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }$
	Gid–3–trip: 90°
	Gid–5/2–stip: 90°
Height	1
Central density	7
Number of external pieces	134
Related polytopes
Army	Semi-uniform Iddip
Regiment	Giddip
Dual	Great rhombic triacontahedral tegum
Conjugate	Icosidodecahedral prism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The great icosidodecahedral prism or giddip, is a prismatic uniform polychoron that consists of 2 great icosidodecahedra, 12 pentagrammic prisms, and 20 triangular prisms. Each vertex joins 1 great icosidodecahedron, 2 pentagrammic prisms, and 2 triangular prisms. As the name suggests, it is a prism based on the great icosidodecahedron.

Vertex coordinates

The vertices of a great icosidodecahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of:

• $\left(0,\,0,\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1}{2}}\right),$

along with all even permutations and all sign changes of the first three coordinates of:

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#917).

• Klitzing, Richard. "giddip".