Non-Flat Regular Polytopes and Restrictions on Chiral Polytopes

[摘要] An abstract polytope is flat if every facet is incident on every vertex. In this paper, we prove that no chiral polytope has flat finite regular facets and finite regular vertex-figures. We then determine the three smallest non-flat regular polytopes in e

[学科分类] 离散数学和组合数学

[关键词] Abstract regular polytope;Chiral polytope;Flat polytope;Tight polytope