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octahedron

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So the h-vector of the boundary of the octahedron is (1, 3, 3, 1).
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As the name suggests, it can be constructed by gyroelongating an octahedron (square bipyramid) by inserting a square antiprism between its congruent halves.
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The rectification of a tetrahedron produces an octahedron.
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At each linked edge two oxygen ions are shared between two octahedra, and each octahedron must have two shared edges to form a chain.
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Each rhenium center is surrounded by an octahedron defined by six oxygen centers.
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For example diamonds, which have a cubic crystal system, are often found as octahedrons.
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The cuboctahedron is a rectified cube and also a rectified octahedron.
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Opposite faces are parallel so, although an octahedron has 8 faces, there are only 4 sets of kamacite plates.
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Each octahedron is rotated by an equal (and opposite, within a pair) angle.
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The intersection of the two tetrahedra form an inner octahedron, which shares the same face-planes as the compound.
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