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《Journal of Hunan University of Arts and Science(Natural Science Edition)》 2015-01
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A rigorous proof on the crystallographic restriction theorem

Zhang Yue;Department of Physics, Hunan Normal University;  
It is significant to find a more rigorous and satisfactory proof of the crystallographic restriction theorem. The inexistence of C5 axis of symmetry is equivalent of that pentagons are impossible to fill all the space with a connected array of pentagons. On the basis of this viewpoint, using a purely mathematical approach the paper rigorously proves that C5 and Cn(n≥7) axes of symmetry can not exist, and one-, two-, three-, four- and six-fold axes of rotational symmetry are allowable, therefore, the axes of symmetry of the crystal can merely exist C1, C2, C3, C4 and C6.
【CateGory Index】: O711
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