Catalan solid

A catalanischer body or dual Archimedean body is a body that behaves in a dual Archimedean body. For example, the rhombic dodecahedron dual to the cuboctahedron. Named are the Catalan body - of which there are thirteen - after the Belgian mathematician Eugène Charles Catalan.

The dual - archimedean solids consist of only one patch type, namely identical non-regular polygons, but have at least two distinct types of corners ( has the rhombic dodecahedron, for example, corners, to the three diamonds, and those of the four diamonds borders ). Thus, they are no archimedean solids in the original sense more.

Allen Catalan bodies in common is that they have an inscribed ball that touches all surfaces from the inside. In addition, an edge ball that touches all edges from inside there. All dihedral angles of a Catalan body are the same.