Large icosidodécaèdre rétroadouci

In Geometry, the large icosidodécaèdre rétroadouci is a Polyèdre not-convex uniform, indexed under the name U₇₄.

Cartesian coordinates

The Cartesian coordinated for the tops of large a icosidodécaèdre rétroadouci 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 smallest real positive solution of ξ ³ −2ξ=−1/τ, or roughly 0,3264046. 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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