Tight polyhedral

报告人简介:Egon Schulte,美国Northeastern University教授,是抽象多边形对称性领域领军学者。

报告学者:Gabriel Kevin Cunningham教授

报告者单位:Wentworth Institute of Technology



报告摘要:It is possible to take the idea of a convex polyhedron and generalize it to a graph structure known as an abstract polyhedron. If there is a fixed p and q such that the faces are all p-cycles and the vertices all have degree q, then the polyhedron is said to be of type {p,q}. In this talk, I will explore the question of finding the smallest abstract polyhedra of each type {p,q}. First we will work completely combinatorially, solving a problem in graph theory. Later, we will define the symmetries of an abstract polyhedron and what it means for an abstract polyhedron to be regular. Then we will try to find small regular polyhedra of each type {p,q}, which is really just a problem in pure group theory. At the end, we will briefly discuss further generalizations of these problems.