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Compound of six decagrammic prisms

This uniform polyhedron compound is a symmetric arrangement of 6 decagrammic 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/√5), ±2τ<sup>−1</sup>, ±√(τ<sup>−1</sup>/√5))
(±(√(τ/√5)+τ<sup>−2</sup>), ±1, ±(√(τ<sup>−1</sup>/√5)−τ<sup>−1</sup>))
(±(√(τ/√5)−τ<sup>−1</sup>), ±τ<sup>−2</sup>, ±(√(τ<sup>−1</sup>/√5)+1))
(±(√(τ/√5)+τ<sup>−1</sup>), ±τ<sup>−2</sup>, ±(√(τ<sup>−1</sup>/√5)−1))
(±(√(τ/√5)−τ<sup>−2</sup>), ±1, ±(√(τ<sup>−1</sup>/√5)+τ<sup>−1</sup>))

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

References

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