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This polyhedron is obtained by successively cutting off each of the vertices of the octahedron or cube.

A cuboctahedron is a semiregular convex polyhedron with two properties:

1. All faces are regular polygons of two types, a triangle, and a square;

2. For any pair of vertices, there is a symmetry of the polyhedron (that is, a motion that translates the polyhedron into itself) that transforms one vertex to another.

Archimedean solids are semiregular polyhedra in the sense that their faces are regular non-similar polygons. Simultaneously, the condition of one of the types of spatial symmetry (tetrahedral, octahedral, or icosahedral) is preserved.

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