Large icosidodécaèdre softened

In Geometry, the large icosidodécaèdre softened is a Polyèdre not-convex uniform, indexed under the name U₅₇.

This polyhedron can be regarded as a Grand icosahedron softened.

Cartesian coordinates

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

(±2α, ±2, ±2β),

(± (α−βτ−1/τ), ± (α/τ+β−τ), ± (−ατ−β/τ−1)),

(± (ατ−β/τ+1), ± (−α−βτ+1/τ), ± (−α/τ+β+τ)),

(± (ατ−β/τ−1), ± (α+βτ+1/τ), ± (−α/τ+β−τ)) and

(± (α−βτ+1/τ), ± (−α/τ−β−τ), ± (−ατ−β/τ+1)),

with an even number of plus signs, where

α = ξ−1/ξ

and

β = −ξ/τ+1/τ²−1/(ξτ),

where τ = (1+√5) /2 is the Golden section (sometimes written φ) and ξ is the negative real solution of ξ ³ −2ξ=−1/τ, or roughly −1,5488772. By taking the odd permutations of the coordinates above with an odd number of plus signs, that gives another form, the énantiomorphe of this polyhedron.

See too

List of the uniform polyhedrons

External bond

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