Internal and external duality in abstract polytopes

Contributions to Discrete Mathematics

Gabe Cunningham ; Mark Mixer

关键词: abstract polytope;    self-dual polytope;    regular polytope;   

学科分类：社会科学、人文和艺术（综合）

来源: University of Calgary * Department of Mathematics and Statistics

【 摘 要 】

We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then, we construct many examples of internally self-dual polytopes. In particular, we show that there are internally self-dual regular polyhedra of each type $\{p, p\}$ for $p \geq 3$ and that there are both infinitely many internally self-dual and infinitely many externally self-dual polyhedra of type $\{p, p\}$ for $p$ even. We also show that there are internally self-dual polytopes in each rank, including a new family of polytopes that we construct here.

【 授权许可】

Unknown