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What are octahedra?

What are octahedra? Here are some definitions.

Noun
  1. plural of octahedron
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Examples
In contrast to crystals that resemble textbook drawings, the most frequently encountered gold crystals are skeletal octahedra.
The structure of boehmite consists of double layers of oxygen octahedra partially filled with Aluminium cations.
The fluorite tends to occur only as cubes modified by the dodecahedron, with simple cubes or octahedra uncommon or absent.
Most that I have seen have been elongated octahedra or other forms, such as some of the branches of an arborescent aggregate.
Peterson and Jordan go on to investigate interesting links between integer octahedra and integer antiprisms.
She notes that lime-green to purplish-green modified fluorite octahedra have been found at this pegmatite.

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