Rhombicuboctahedron

Rhombicuboctahedron
Type	Archimedean Uniform polyhedron
Faces	8 equilateral triangles 18 squares
Edges	48
Vertices	24
Vertex configuration	${\displaystyle 24(3\cdot 4^{3})}$
Schläfli symbol	${\displaystyle r{\begin{Bmatrix}3\\4\end{Bmatrix}}}$
Symmetry group	Octahedral symmetry ${\displaystyle \mathrm {O} _{\mathrm {h} }}$ Pyritohedral symmetry ${\displaystyle \mathrm {T} _{\mathrm {h} }}$
Dihedral angle (degrees)	square-to-square: 135° square-to-triangle: 144.7°
Dual polyhedron	Deltoidal icositetrahedron
Vertex figure
Net

In geometry, the rhombicuboctahedron is an Archimedean solid with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named by Johannes Kepler in his 1618 Harmonices Mundi, being short for truncated cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron.^[1]

The rhombicuboctahedron is an Archimedean solid, and its dual is a Catalan solid, the deltoidal icositetrahedron. The elongated square gyrobicupola is a polyhedron that is similar to a rhombicuboctahedron, but it is not an Archimedean solid because it is not vertex-transitive. The rhombicuboctahedron is found in diverse cultures in architecture, toys, the arts, and elsewhere.