组合多面体理论及几何构型设计

根据目前国内网壳形式的现状,提出了一种全部由五边形和六边形网格组成的网壳形式(以下简称组合多面体).本文首先论述了组合多面体的几何性质,其几何性质的对称性和均匀性为它的实际应用提供了前提条件;然后又总结了这种组合多面体的面数计算公式,说明这样的组合多面体有无穷多个;之后根据节点突角和相等原理,分别算出了32面体,42面体,92面体,122面体的六边形构型,节点构型,杆长类型和突角和,又列出了162面体,252面体,272面体,482面体,752面体的这种性质,进而总结了这些特性间的关系,为组合多面体的建模提供了依据.

Theory and Geometry Configuration Design of Combination Polyhedrons

According to the present and domestic situation of the net shell,this paper proposes one kind of net shell which is composed of pentagons and hexagons (combination polyhedrons).This paper elaborates geometric properties of the combination polyhedrons.The symmetry and the uniformity of the geometric properties provide the premise for its practical application.Then,the equation of the surface number of the combination polyhedrons is summarized.This shows such combination polyhedrons are infinite.Next this paper gives the hexagon configurations, the node configurations,the pole types and the quoin sum of the 32-hedron,42-hedron,92-hedron,122-hedron based on the principle of the quoin sum equaling.These kinds of nature of the 162-hedron,252-hedron,272-hedron,482-hedron and 752-hedron have also been listed.Finally,this article summarizes the relations of these characters which provide the basis for the modeling of the combination polyhedrons.