中文摘要：

以羊毛纤维和人类头发为原型，以超级分形纤维概念为基础，抽象出了（3）分圆和（9＋2）分圆分形集，构造了（3，9＋2）分圆和（9＋2，3）分圆双重分形集．针对（9＋2）拓扑花样，证明了这样的命题：（9＋2）拓扑花样精确地存在，但不唯一，其总个数为9，其中有2种同素异构体，即9种拓扑花样中，只有2种是独立（或基本）的．另外证实了（3，9＋2）或（9＋2，3）分圆分形花样是一个对称性破缺的黄金分形．

英文摘要：

Based on the concepts of fractal super fibers, the （3,9 ＋ 2）-circle and （9 ＋ 2,3）-circle bi- nary fractal sets were abstracted from such prototypes as wool fibers and human hairs, with the （3）- circle and the （9 ＋ 2）-circle fractal sets as subsets. As far as the （9 ＋ 2） topological patterns are concemed, the following propositions were proved： The （9 ＋ 2） topological patterns acogat~ly exist, but theyare of no uniqueness. Their total number is 9. Among them there are only 2 allotropes. In anoth- er word, among the 9 topological patterns only 2 are independent （or fundamental）. Besides, it was demonstrated that the （3,9 ＋ 2 ） -circle and （9 ＋ 2,3 ） -circle fractal sets are golden ones with symmetry breaking.