Regular and chiral polytopes

规则和手性多面体

• 批准号: 8857-2006
• 负责人: Weiss, AsiaIvic
• 金额: $ 0.58万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=389852
• 关键词: Regular; chiral; polytopes

Most of my research deals with the interplay between geometry, combinatorics and group theory.  In this context I study abstract polytopes, which are combinatorial structures that generalize the classical polytopes i.e. higher dimensional polyhedra.  As of recently I also study symmetric and semisymmetric graphs.  Graph theory owes many powerful ideas to geometry and now we explore a way in which graphs can be embedded in polytopes.  Of particular interest are chiral polytopes, which have maximal symmetry by rotation (in contrast with regular polytopes which have maximal symmetry by reflection) and hence come in two enantiomorphic forms, that is in left- and right-handed versions. These are fundamental geometric objects, which in my opinion have great potential for applications in crystallography, biology, chemistry and physics.  Because of their high degree of symmetries they also have great aesthetic appeal.

我的大部分研究涉及几何学，组合学和群论之间的相互作用。在这种情况下，我研究抽象多面体，这是组合结构，推广了经典的多面体，即高维多面体。最近，我还研究了对称和半对称图。图论欠几何许多强大的思想，现在我们探索一种方法，其中图可以嵌入多面体。特别令人感兴趣的是手征多面体，其通过旋转具有最大对称性（与通过反射具有最大对称性的规则多面体相反），因此具有两种对映体形式，即左手和右手形式。这些都是基本的几何物体，在我看来，它们在晶体学、生物学、化学和物理学中有着巨大的应用潜力，因为它们的高度对称性，它们也有着巨大的美学吸引力。