Perfect image point cloud

...When viewed microscopically, there are 230 possible space groups for a crystal, but when viewed macroscopically, their symmetry is limited to 32 point groups, which are called crystal families or crystal classes.
[Crystal system]
If we search for a point group that contains all the symmetry operations that can be performed by moving a space lattice with one of its lattice points fixed, we obtain the seven types in the fourth column of the table, which are called perfect image point groups. The crystal lattice that is superimposed on itself by these point groups has symmetry reflected in the direction and period of its lattice lines, so from now on, we will also replace the crystal axes with the direction of the lattice lines that represent symmetry.

*Some of the terminology explanations that refer to "perfect image point cloud" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…結晶を微視的に見た場合，空間群は230種類可能であったが，巨視的に見るとその対称は32種の点群に限られ，これらを結晶族または晶族という。
［結晶系］
　空間格子の格子点の一つを固定しての運動によって，格子をそれ自身に重ね合わすような対称操作をすべて含む点群を求めると，表における第4列の7種のものが得られ，これらを完面像点群(晶族)という。これらの点群によってそれ自身に重ねられる結晶格子は，その格子線の方向や周期が対称を反映しており，今後は結晶軸も対称を表す格子線の方向にとりかえることにする。…

※「完面像点群」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典 第２版について | 情報