Great icosihemidodecahedral prism

Great icosihemidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Geihiddip
Coxeter diagram	/2 ((x x5/3x3/2o3*b)/2)
Elements
Cells	20 triangular prisms, 6 decagrammic prisms, 2 great icosihemidodecahedra
Faces	40 triangles, 60 squares, 12 decagrams
Edges	30+120
Vertices	60
Vertex figure	Bowtie pyramid, edge lengths 1, √(5–√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{7-2\sqrt5}}{2} ≈ 0.79496$
Dichoral angles	Geihid–3–trip: 90°
	Geihid–10/3–stiddip: 90°
	Trip–4–stiddip: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ$
Height	1
Number of pieces	182
Related polytopes
Army	Semi-uniform Iddip
Regiment	Giddip
Dual	Great icosihemidodecacronic tegum
Conjugate	Small icosihemidodecahedral prism
Abstract properties
Euler characteristic	–2
Topological properties
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The great icosihemidodecahedral prism or geihiddip, is a prismatic uniform polychoron that consists of 2 great icosihemidodecahedra, 20 triangular prisms, and 6 decagrammic prisms. Each vertex joins 1 great icosihemidodecahedron, 2 triangular prisms, and 2 decagrammic prisms. As the name suggests, it is a prism based on the great icosihemidodecahedron.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#919).