Truncated great icosahedron


In geometry, the truncated great icosahedron is a nonconvex uniform polyhedron, indexed as U55. It has 32 faces, 90 edges, and 60 vertices. It is given a Schläfli symbol t or t0,1 as a truncated great icosahedron.

Cartesian coordinates

for the vertices of a truncated great icosahedron centered at the origin are all the even permutations of
where τ = /2 is the golden ratio. Using 1/τ2 = 1 − 1/τ one verifies that all vertices are on a sphere, centered at the origin, with the radius squared equal to 10−9/τ. The edges have length 2.

Related polyhedra

This polyhedron is the truncation of the great icosahedron:
The truncated great stellated dodecahedron is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and 12 pentagonal faces as truncations of the original pentagram faces, the latter forming a great dodecahedron inscribed within and sharing the edges of the icosahedron.
NameGreat
stellated
dodecahedron		Truncated great stellated dodecahedronGreat
icosidodecahedron		Truncated
great
icosahedron		Great
icosahedron
Coxeter-Dynkin
diagram
Picture

Great stellapentakis dodecahedron

The great stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great icosahedron. It has 60 intersecting triangular faces.