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The compound of eight octahedra with rotational freedom is a uniform polyhedron compound. It is composed of a symmetric arrangement of 8 octahedra, considered as triangular antiprisms. It can be constructed by superimposing eight identical octahedra, and then rotating them in pairs about the four axes that pass through the centres of two opposite octahedral faces. Each octahedron is rotated by an equal angle θ.
It can be constructed by superimposing two compounds of four octahedra with rotational freedom, one with a rotation of θ, and the other with a rotation of −θ.
When θ = 0, all eight octahedra coincide. When θ is 60 degrees, the octahedra coincide in pairs yielding the compound of four octahedra.
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