Cuboctahedron

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In geometry, a cuboctahedron is a polyhedron with eight triangular faces and six square faces. A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such it is a quasiregular polyhedron, i.e. an Archimedean solid, being vertex-transitive and edge-transitive.

Its dual polyhedron is the rhombic dodecahedron.

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Area and volume

The area A and the volume V of the cuboctahedron of edge length a are:

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Cartesian coordinates

The Cartesian coordinates for the vertices of a cuboctahedron (of edge length √2) centered at the origin are:

An alternate set of coordinates can be made in 4-space, as 12 permutations of:

This construction exists as one of 16 orthant facets of the cantellated 16-cell.

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