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Compound of six decagonal prisms

This uniform polyhedron compound is a symmetric arrangement of 6 decagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±√(τ<sup>−1</sup>/√5), ±2τ, ±√(τ/√5))
(±(√(τ<sup>−1</sup>/√5)−τ<sup>2</sup>), ±1, ±(√(τ/√5)+τ))
(±(√(τ<sup>−1</sup>/√5)−τ), ±τ<sup>2</sup>, ±(√(τ/√5)+1))
(±(√(τ<sup>−1</sup>/√5)+τ), ±τ<sup>2</sup>, ±(√(τ/√5)−1))
(±(√(τ<sup>−1</sup>/√5)+τ<sup>2</sup>), ±1, ±(√(τ/√5)−τ))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

References

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