Polytope operations

This is an incomplete list of operations that can be done to polytope s, presented in the framework of Coxeter-Dynkin diagram s. They are typically done to regular polytope s and produce Wythoffian uniform polytope s.

The number(s) in the "prefix" associated with each operation indicate which node(s) of the Coxeter-Dynkin diagram the operation "rings."

Since a polytope's diagram has a number of nodes equal to the polytope's dimension, an N-dimensional polytope can only use operations with "prefix numbers" less than N. (Since 0 is one of them, it makes sense.) In addition, the names of some operations are typically not used until even higher dimensions than this rule suggests. For example, rectified polygons are simply called "dual" even though polygons can be rectified, and even though node 2 of rox is ringed it is not referred to as a "birectified hi."