Higher symmetries frequently amaze human beings because of the illusions and incredible landscapes such symmetries can produce. For example, imagine the unearthly pictures of the Dutch graphic artist M.C. Escher. He made use of glide symmetry and reflection to produce unbelievable transitions and transformations of objects and beings, as illustrated in Figure 1(a). However, the history of higher symmetries started much earlier. Escher was partially inspired by the Moorish tessellations in the Alhambra in Granada, Spain, such as the ones pictured in Figure 1(b).

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具有更高对称性的周期结构：它们在电磁器件中的应用

更高的对称性经常让人类惊叹，因为这种对称性可以产生幻觉和令人难以置信的风景。例如，想象一下荷兰图形艺术家 MC Escher 的超凡脱俗的照片。他利用滑动对称性和反射来产生令人难以置信的物体和生物的过渡和变换，如图 1(a) 所示。然而，更高对称性的历史开始得更早。埃舍尔的部分灵感来自西班牙格拉纳达阿尔罕布拉宫的摩尔镶嵌，如图 1(b) 所示。