Rhombicuboctahedron

+

+This remarkable shape can be derived from either a [cube](/wiki/cube) or an [octahedron) through a process of expansion. More specifically, it can be obtained by expanding a [cuboctahedron](/wiki/cuboctahedron) (another Archimedean solid) by pulling its faces apart and inserting new square faces in the gaps. Its dual polyhedron is the [Deltoidal Icositetrahedron](/wiki/deltoidal_icositetrahedron), a shape with 24 kite-shaped faces. The Rhombicuboctahedron exhibits [octahedral symmetry](/wiki/octahedral_symmetry), reflecting its close relationship to the cube and octahedron, and is a [uniform polyhedron](/wiki/uniform_polyhedron).

+The name "Rhombicuboctahedron" hints at its geometric origins. The "rhombi" part refers to the square faces, and "cuboctahedron" refers to the [cuboctahedron](/wiki/cuboctahedron), from which it can be expanded. It is a [convex](/wiki/convex) polyhedron, meaning all its interior angles are less than 180 degrees. This shape appears in various contexts, from the facets of [crystals](/wiki/crystal) to components in [mechanical design](/wiki/mechanical_design) and [architecture](/wiki/architecture), showcasing its practical and aesthetic appeal.

+- [Cuboctahedron](/wiki/cuboctahedron)

+- [Deltoidal Icositetrahedron](/wiki/deltoidal_icositetrahedron)

+The Rhombicuboctahedron is a captivating [Archimedean solid](/wiki/archimedean_solid), a harmonious dance of squares and triangles. It features 26 faces in total: 18 [square](/wiki/square) faces and 8 [triangle](/wiki/triangle) faces. These faces meet at 24 uniform [vertices](/wiki/vertex), with each vertex surrounded by one triangle and three squares (a configuration often denoted as 3.4.4.4). It possesses 48 [edges](/wiki/edge), and its entire structure reveals a perfectly symmetrical [polyhedron](/wiki/polyhedron) of balanced beauty.

+This remarkable shape can be derived from either a [cube](/wiki/cube) or an [octahedron](/wiki/octahedron) through a process of expansion. Imagine a cube where each face is pushed outwards, and the gaps are filled with squares and triangles. Its dual polyhedron is the [Deltoidal Icositetrahedron](/wiki/deltoidal_icositetrahedron), a shape with 24 kite-shaped faces. The Rhombicuboctahedron exhibits [octahedral symmetry](/wiki/octahedral_symmetry), reflecting its close relationship to the cube and octahedron.

+- [Octahedron](/wiki/octahedron)

+The Rhombicuboctahedron is a captivating [Archimedean solid](/wiki/archimedean_solid), a harmonious dance of squares and triangles. Each of its 26 faces meets at uniform vertices, revealing a perfectly symmetrical [polyhedron](/wiki/polyhedron) of balanced beauty.

+## See also

+- [Archimedean Solid](/wiki/archimedean_solid)

+- [Polyhedron](/wiki/polyhedron)

+- [Cuboctahedron](/wiki/cuboctahedron)