cubooctahedral

The cuboctahedron is a polyhedron with 12 faces, 24 edges, and 12 vertices. It is an Archimedean solid, meaning it is one of the 13 convex polyhedra whose faces are regular polygons of two or more types. The cuboctahedron is dual to the rhombic dodecahedron, meaning that the vertices of one correspond to the faces of the other, and vice versa. It can be constructed by truncating the vertices of a cube, resulting in eight triangular faces and six square faces. Alternatively, it can be derived from an octahedron by truncating its vertices, yielding six triangular faces and eight square faces. The cuboctahedron is also known as a truncated cube or truncated octahedron. It has applications in various fields, including crystallography, where it represents a common crystal structure, and in architecture, where it is used in the design of certain buildings. The cuboctahedron is a fascinating geometric shape that combines elements of both cubic and octahedral structures.