Rhombicuboctahedron | |
---|---|
Type | Archimdean Uniform polyhedron |
Faces | 8 equilateral triangles 18 squares |
Edges | 48 |
Vertices | 24 |
Vertex configuration | |
Schläfli symbol | |
Symmetry group | Octahedral symmetry Pyritohedral symmetry |
Dihedral angle (degrees) | square-to-square: 135° square-to-triangle: 144.7° |
Dual polyhedron | Deltoidal icositetrahedron |
Vertex figure | |
Net | |
In geometry, rhombicuboctahedron is an Archimedean solid with 26 faces, consisting of 8 equilateral triangles and 18 squares. It is 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 it has Catalan solid as its dual, 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 skeleton of a rhombicuboctahedron can be represented as a graph. The rhombicuboctahedron is found in diverse cultures in architecture, toys, the arts, and elsewhere.
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