规整多面体空间填充的分析探究

Analysis on regular polyhedral space filling

为了探寻能通过空间阵列组成密实堆积体来填充整个三维空间的空间填充多面体,从棱柱开始进行研究,特别对正棱柱进行了各种有趣的对称切补,得到了一些实用的空间填充多面体.同时,运用数学模型分析了菱形十二面体和截角八面体,说明它们是两种优良的空间无缝填充单体.然后,利用多面体的二面角公式,探究了正多面体和半正多面体等规整多面体的组合填充,发现了12种组合填充模型,为空间多面体的填充以及空间结构的搭建储备了一些可以利用的理论原型.

In order to find space-filling polyhedrons which can form a dense accumulated structure to fill the space through spatial arrays,a research on prisms was conducted.In particular,various interesting symmetric cut-and-fills were operated on the regular prisms.By doing that,the researcher got some practical space filling polyhedrons.Meanwhile,it is found that rhombic dodecahedron and truncated octahedron are two excellent spatial seamless filled monomers while mathematical models are utilized.In addition,twelve kinds of combined models were discovered by researching the combination of regular polyhedrons and semi regular polyhedrons with the help of the dihedral angle formula.This finding provides some practical theoretical prototypes for the filling of spatial polyhedrons and the building of spatial structures.