传统的固体理论认为，晶体应具有周期性平移对称和旋转对称。就像生活中不能用五角形拼块铺满地面一样，晶体结构不允许出现五次或六次以上的对称。可是，在１９８４年夏，中国科学院金属研究所的郭可信和他的学生们，利用１００万倍的电子显微镜，在纳米这个原子尺度上对含钛 The traditional solid theory holds that the crystals should have periodic translational symmetry and rotational symmetry. Just as life can not be covered with pentagonal tiles, the crystal structure does not allow five or more symmetries. However, in the summer of 1984, Guo Kexin and his students at the Institute of Metal Research, Chinese Academy of Sciences, used a one-million-times electron microscope to inspect titanium-containing titanium