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octahedron

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Note the duality between cube and octahedron, and between dodecahedron and icosahedron.

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Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices.

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The tetrahedron, octahedron, icosahedron, and great icosahedron appear commonly in non-prismatic uniform polychora, but not in their snub constructions.

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The basic structure forms stacked sheets of linked octahedrons of aluminium hydroxide.

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Its shape is derived from a stellated octahedron, but the tips of the vertices are truncated to form small triangles.

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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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In addition, by duality with the octahedron, the cube, which is usually regular, can be made quasiregular if alternate vertices are given different colors.

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The "tetragonal trisoctahedron" is another name for the deltoidal icositetrahedron, a different polyhedron with three quadrilateral faces for every face of an octahedron.

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So the h-vector of the boundary of the octahedron is (1, 3, 3, 1).

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The octahedron shares two of its opposite faces with that of neighbouring vanadinite units, forming a continuous chain of octahedrons.

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