Conway polyhedron notation

The Conway polyhedron notation is a way to represent polyhedra with high symmetries. One starts with a "seed" polyhedron and modifies it with a series of "operators" to obtain the desired polyhedron. These modifications involve subdividing existing faces into new element s, and sometimes removing old elements. The notation itself is a string of mostly letters, representing the seed polyhedron as an uppercase letter on the right-hand side of the string, and operators as lowercase letters that are applied from right to left.

The notation is not meant to describe nonconvex polyhedra (although certain implementations of it can produce nonconvex results, and its operators can be applied to tilings on any 2D surface). It has not been applied to dimensions other than 3. The Platonic solids can be represented as Conway operators applied to prisms, antiprisms, and pyramids. The Archimedean and Catalan solids can also be represented as Conway operators applied to Platonic solids. (Applying these to the tetrahedron might result in a Platonic solid.) The wide variety of possibilities by which new faces, edges, and vertices can be created and by which old ones can be removed may give rise to many different operators from different sources. Some are not default or standardized, and might have conflicting notation or might not be found in all implementations of the Conway notation.