以數學方法標示晶體的晶格點及分析對稱性－－簡單立方與體心立方

Analyze Symmentry of the Crystals by Orienting Mathematically the Lattice Points-Simple Cubic and Body-Centered Cubic

本文是以數學方法來標示簡單立方SC(simple cubic)及體心立方BCC(body-centered cubic二種晶體在(111)平面上晶格點(lattice)座標及分析相對[1, 1, 1]方向軸位置與對稱性，邏輯清楚易懂且具嚴謹性。此外本方法討論的固態晶體對稱性不僅適用於立方晶體，也可擴展到其他更複雜的晶體與方向軸。

This paper illustrates the symmetry of crystals about the [1, 1, 1] axis of simple cubic and the body-centered cubic crystals by orientation of the lattice points on (111) planes. Since mathematical principles were introduced, it offers logical thinking and ought to be understood lucidly and thoroughly. The same medium can be also adopted to characterize the symmetry about other axes and more complicated crystals.