Convex Polytopes

一个集合S是凸的，如果对于S中的任意两点，由这两点确定的直线段也包含在S中。凸多面体P是由有限点集确定的最小凸集。因此，三角形是由平面（二维）中的三个点确定的凸多面体，立方体是由空间（三维）中的八个点确定的凸多面体 研究凸多面体的几何和组合性质，其长期目标是：验证对偶相邻多面体的Gohberg-Markus-Hadwiger猜想，发展多面体的组合理论和理解多面体的几何结构。 短期目标是研究某些类的多面体（循环的），验证对偶相邻4-多面体和对偶全缝合d-多面体的G-M-H猜想，确定边对映4-多面体的最大顶点数。 这些项目的预期合作者是M。Bayer（堪萨斯），K. Boroczky（布达佩斯），F. Fodor（Szeged），A. Heppes（布达佩斯），D. Oliveros（墨西哥），以及研究生和博士后。

A set S is convex if for any two points in S, the straight line segment determined by the two points is also contained is S. A convex polytope P is the smallest convex set determined by a finite set of points.Thus, a triangle is a convex polytope determined by three points in a plane ( 2-dimensional) and a cube is a convex polytope determined by eight points in space( 3-dimensional) An investigation of the geometric and combinatorial properties of convex polytopes with the following long tern objectives: verification of the Gohberg-Markus-Hadwiger Conjecture for dual neighbourly polytopes, development of a combinatorial theory of polytopes and understanding the geometrical structure of polytopes. The short term objectives are the investigation of certain classes of polytopes ( periodically-cyclic), the verification of the G-M-H Conjecture for dual neighbourly 4-polytopes and dual totally-sewn d-polytopes and determining the maximum number of vertices of edge-antipodal 4-polytopes. Anticipated collaborators for these projects are M. Bayer( Kansas), K. Boroczky ( Budapest),F. Fodor ( Szeged), A. Heppes ( Budapest), D. Oliveros ( Mexico), as well as graduate students and post-docs.