Skeletal Polyhedra, Geometric Graphs, and Symmetry

报告学者:Egon Schulte教授

报告者单位:Northeastern University



报告摘要:The study of highly symmetric structures in Euclidean 3-space has a long and fascinating history tracing back to the early days of geometry. With the passage of time, various notions of polyhedral structures have attracted attention and brought to light new exciting figures intimately related to finite or infinite groups of isometries. A new graph-theoretical (or skeletal) approach to polyhedra was pioneered by Grunbaum in the 1970's and builds on Coxeter's work. These skeletal polyhedra are viewed not as solids but rather as finite or infinite periodic geometric edge graphs in space equipped with additional polyhedral super-structure imposed by the faces. Since the mid 1970's there has been a lot of activity in this area. Much work has focused on classifying skeletal polyhedra and skeletal complexes by symmetry, with the degree of symmetry determined by distinguished transitivity properties of the geometric symmetry groups. These skeletal figures exhibit fascinating geometric, combinatorial, and algebraic properties and include many new finite and infinite structures. The talk gives an introduction to this area.