Through careful analysis on the cross-section of sisal fibers, it is found that the middle lamellae between the cell walls have clear geometric characteristics: between the cell walls of three neighboring cells, the m...Through careful analysis on the cross-section of sisal fibers, it is found that the middle lamellae between the cell walls have clear geometric characteristics: between the cell walls of three neighboring cells, the middle lamellae form a three-way junction with 120° symmetry. If the neighboring three-way junctions are connected, a network of Steiner tree with angular symmetry and topological invariability is formed. If more and more Steiner trees are connected, a network of Steiner rings is generated. In another word, idealized cell walls and the middle lamellae are dominated by the Steiner geometry. This geometry not only depicts the geometric symmetry, the topological invariability and minimal property of the middle lamellae, but also controls the mechanics of sisal fibers.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10602040, 10872114)
文摘Through careful analysis on the cross-section of sisal fibers, it is found that the middle lamellae between the cell walls have clear geometric characteristics: between the cell walls of three neighboring cells, the middle lamellae form a three-way junction with 120° symmetry. If the neighboring three-way junctions are connected, a network of Steiner tree with angular symmetry and topological invariability is formed. If more and more Steiner trees are connected, a network of Steiner rings is generated. In another word, idealized cell walls and the middle lamellae are dominated by the Steiner geometry. This geometry not only depicts the geometric symmetry, the topological invariability and minimal property of the middle lamellae, but also controls the mechanics of sisal fibers.
