中文摘要：

在在有旋转的不同对称操作的比表面精力的各种各样的条件下面的破裂角度上的计算以后，水晶的结构上的分数维的尺寸的依赖的复杂行为被显示出。裂缝宣传最弱的水晶飞机，这被发现如果 anisotropy 是足够地强壮的，不管最大的压力的方向是什么；然后，折断的表面的分数维的尺寸可能被近似分数维的结构决定已经在材料存在。折断的表面的分数维的尺寸的特性将是容易的出现在这种情况中。相对地，裂缝宣传最大的压力的方向如果 anisotropy 是足够地弱的，不管飞机是最弱的水晶的方向。折断的表面的分数维的尺寸的普遍性将是可能的出现在这种情况中。在许多真实材料，材料的普遍性和特性被联系。测量的分数维的尺寸可以被材料的结构差不多影响，它通过材料的特性显示出它的普遍性。

英文摘要：

After calculation on the fracture angles under various conditions of specific surface energies with different symmetry operations of rotation, the complicated behavior of dependence of fractal dimension on the structure of crystal is shown. It is found that the crack propagates along the weakest crystal plane no matter what the direction of the maximum stress is if the anisotropy is sufficiently strong; and then, the fractal dimension of the fractured surfaces might be determined by the approximate fractal structure already existed in the material. Specificity of the fractal dimension of fractured surfaces would be easy to appear in this case. Reversely, the crack propagates along the direction of the maximum stress no matter what direction of the weakest crystal plane is if the anisotropy is sufficiently weak. Universality of the fractal dimension of fractured surfaces would be possible to appear in this case. In many real materials, universality and specificity of the materials are associated. The fractal dimension measured may more or less be influenced by the structure of materials and it shows its universality through the specificity of materials.