Coxeter notationIn geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups. The notation is named after H. S. M. Coxeter, and has been more comprehensively defined by Norman Johnson. For Coxeter groups, defined by pure reflections, there is a direct correspondence between the bracket notation and Coxeter-Dynkin diagram.
1 22 polytopeDISPLAYTITLE:1 22 polytope In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named as V72 (for its 72 vertices). Its Coxeter symbol is 122, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequence. There are two rectifications of the 122, constructed by positions points on the elements of 122. The rectified 122 is constructed by points at the mid-edges of the 122.
4 21 polytopeDISPLAYTITLE:4 21 polytope In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 8-ic semi-regular figure. Its Coxeter symbol is 421, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 4-node sequences, . The rectified 421 is constructed by points at the mid-edges of the 421. The birectified 421 is constructed by points at the triangle face centers of the 421.
