Gosset 3 21 polytope: Semiregular polyhedron, Edmund Hess, Thorold Gosset, Coxeter–Dynkin diagram, Harold Scott MacDonald Coxeter, N-skeleton, Uniform polytope - Tapa blanda

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In 7-dimensional geometry, the 321 is a semiregular polytope, enumerated by Thorold Gosset in his 1900 paper. He called it an 7-ic semi-regular figure. It is called the Hess polytope for Edmund Hess who first discovered it. Its construction is based on the E7 group. Coxeter named it as 321 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 3-node sequence. For visualization this 7-dimensional polytope is often displayed in a special skewed orthographic projection direction that fits its 56 vertices within a 18-gonal regular polygon (called a Petrie polygon). Its 756 edges are drawn between 3 rings of 18 vertices, and 2 vertices in the center. Specific higher elements (faces, cells, etc) can also be extracted and drawn on this projection. The 1-skeleton of the 321 polytope is called a Gosset graph.