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Compound of twenty octahedra with rotational freedom

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  1. This uniform polyhedron compound is a symmetric arrangement of 20 octahedra, considered as triangular antiprisms

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  2. Cartesian coordinates for the vertices of this compound are all the cyclic permutations of where τ = (1+√5)/2 is the golden ratio (sometimes written φ)

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  3. can be constructed by superimposing two copies of the compound of 10 octahedra UC16, and for each resulting pair of octahedra, rotating each octahedron in the pair by an equal and opposite angle θ

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  4. When θ is zero or 60 degrees, the octahedra coincide in pairs yielding (two superimposed copies of) the compounds of ten octahedra UC16 and UC15 respectively

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  5. At a certain intermediate angle the vertices coincide in pairs, yielding the compound of twenty octahedra (without rotational freedom)

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
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