rhombicuboctahedron

The rhombicuboctahedron, also called the small rhombicuboctahedron, is an Archimedean solid with 26 faces: eight equilateral triangles and eighteen squares. It has 24 vertices and 48 edges. All faces are regular, and the solid is uniform and highly symmetric, possessing octahedral symmetry (Oh). At each vertex, one triangle and three squares meet, giving a vertex figure composed of a triangle adjacent to three squares.

Construction and relations: The rhombicuboctahedron can be obtained by cantellating a cube, which expands each edge to create a new square face while preserving the original faces as squares and introducing triangular faces at the cube’s vertices. It is also related to other uniform solids through operations like truncation and cantellation applied to cube- and cuboctahedron-based forms. The dual polyhedron of the rhombicuboctahedron is the deltoidal icositetrahedron (also known as the trapezoidal icositetrahedron), which has 24 kite-shaped faces.

Summary: As one of the Archimedean solids, the rhombicuboctahedron combines triangular and square faces in a highly regular arrangement, with uniform vertices and substantial symmetry. It serves as a classic example of a polyhedron that blends two regular polygons into a single, highly symmetrical form, and it appears in geometric modeling, crystallography contexts, and various decorative and educational settings.