Generalized Crystallography of Rod Systems

有足够长的圆柱杆按一定的顺序排列。其动机是构建一种广义结晶学，它将周期和非周期排列统一起来。它汇编了排列和堆积的基本知识，这是物理世界中的基本现象。系统地研究了具有相当高密度和/或高对称性的杆的可能的周期性排列。棒的方向被限制为n种，其中n=3、4、6，例如称为3-AXS排列等。3-AXSCase相当简单。在4轴的情况下，高对称性和高密度是另一个问题。对6-AXS的情况进行了深入的研究，并在一定条件下对可能的结构进行了详尽的研究。虽然调查并不完善，但仍在进行中。引入了支持和自我支持的概念。本课题涉及许多领域，如复合材料、石榴石等结构相当复杂的结晶学。

Cylindrical rods with long enough are arranged in some order. The motivation is to construct a generalized crystallography, which unifies periodic and nonperiodic arrangements. It serves as compilation of basic knowledge of arranging and packing, which are fundamental phenomena in physical world.A systematic investigation is done focusing on the possible periodic arrangements of rods with rather high density and/or high symmetry. The directions of rods are restricted to a n kinds, where n=3,4,6, which are, for example, referred to as 3-axs arrangement and so on. The 3-axscase is rather simple. In the 4-axs case, high symmetry and high density are another problem. The 6-axs case is intensively investigated and the possible structures are exhaustively studied within a certain condition. Though the investigation is not perfect and is still going on.The concepts of support and self-support are introduced. The present subject has relationship with many fields ; for example, composite materials, crystallography of rather complex structure like garnet.