Large truncated icosahedron

In Geometry, the large icosahedron truncated is a Polyèdre not-convex uniform, indexed under the name U₅₅.

This polyhedron is the truncation Grand icosahedron.

Cartesian coordinates

The Cartesian coordinated for the tops of a large truncated icosahedron centered in the beginning are all the even permutations of

(±1, 0, ±3/τ)

(±2, ±1/τ, ±1/τ³)

(± (1+1/τ²), ±1, ±2/τ)

where τ = (1+√5) /2 is the Golden section (sometimes written φ). By using 1/τ ² = 1 − 1/τ, one checks that all the tops are on a Sphère, centered in the beginning, with the ray raised with the square equal to 10−9/τ. The edge is length 2.

See too

List of the uniform polyhedrons

External bond

Random links: