Great icosahedral pyramid

Great icosahedral pyramid
Rank	4
Type	Segmentotope
Notation
Bowers style acronym	Gikepy
Coxeter diagram	oo5/2oo3ox&#x
Elements
Cells	20 tetrahedra, 1 great icosahedron
Faces	20+30 triangles
Edges	12+30
Vertices	1+12
Vertex figures	1 great icosahedron, edge length 1
	12 pentagrammic pyramids, edge length 1
Measures (edge length 1)
Circumradius	${\frac {{\sqrt {5}}-1}{2}}\approx 0.61803$
Height	${\frac {1+{\sqrt {5}}}{4}}\approx 0.80902$
Related polytopes
Army	non-RF Ikepy
Regiment	Sissidpy
Dual	Great stellated dodecahedral pyramid
Conjugate	Icosahedral pyramid
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3×I, order 120
Convex	No
Nature	Tame

The great icosahedral pyramid, or gikepy, a non-convex segmentotope. It has 20 regular tetrahedra and 1 regular great icosahedron as cells. As the name suggests, it is a pyramid based on the great icosahedron.

It is the first segment of the grand hexacosichoron in vertex-first orientation.

External links

• Klitzing, Richard. "gikepy".