The polyhedron is obtained based on the mathematical expansion (for more detail, No. 21 of the Magic Edges).

A truncated cuboctahedron is a semiregular polyhedron with two properties:
1. All faces are regular polygons of three types - an octagon, a hexagon, and a quadrilateral;
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.

The truncated cuboctahedron is one of the 13 solids of Archimedes.

Archimedean solids are semiregular polyhedra because their faces are regular polygons. Still, they are not the same, while the condition of one of the types of spatial symmetry (tetrahedral, octahedral or icosahedral) is preserved.