Arbitrarily Large Neighborly Families of Congruent Symmetric Convex 3-Polytopes
Arbitrarily Large Neighborly Families of Congruent Symmetric Convex 3-Polytopes
复制标题
全等对称凸3-多面体的任意大邻域族
DOI：
--
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Jeff Erickson
中科院分区：
文献类型：
--
作者：
Jeff Erickson
对于任意正整数n，我们在R^3中构造一族n个全等凸多面体，使得每对多面体相交于一个公共小平面。以前，最大的此类族仅包含八个多面体。我们的多面体是螺旋线上均匀分布的点的Voronoi区域（t，cos t，sin t）。通过一个简单的修改，我们可以确保族中的每个多面体都有一个点、一条线和一个对称面。我们还推广我们的建设更高的维度，并介绍了一个新的家庭循环多面体。
We construct, for any positive integer n, a family of n congruent convex polyhedra in R^3, such that every pair intersects in a common facet. Previously, the largest such family contained only eight polytopes. Our polyhedra are Voronoi regions of evenly distributed points on the helix (t, cos t, sin t). With a simple modification, we can ensure that each polyhedron in the family has a point, a line, and a plane of symmetry. We also generalize our construction to higher dimensions and introduce a new family of cyclic polytopes.