In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations. Conway and Hart extended the idea of using operators, like truncation as defined by Kepler, to build related polyhedra of the same symmetry. For example, tC represents a truncated cube, and taC, parsed as , is (topologically) a truncated cuboctahedron. The simplest operator dual swaps vertex and face elements; e.g., a dual cube is an octahedron: dC=O. Applied in a series, these operators allow many higher order polyhedra to be generated. Conway defined the operators abdegjkmost, while Hart added r and p. Later implementations named further operators, sometimes referred to as "extended" operato