On Euclidean space, the A4 size paper as well as other Silver Rectangle with aspect ratio √ 1: √ 2 , can be wrapped into 2^N and 2(2N+1) ^ 2 congruent tetrahedrons for each face. The rectangular area equals to its wrapped surface area of all tetrahedron. In other words, the rectangle can be bent and folded into 4N same unit of an isosceles triangle small pieces to form the N of the similar tetrahedron. This kind of tetrahedron is that surrounded by the similar one where space can be filled with this isosceles tetrahedron. There are only two kinds of edge and its ratio is √ 3 :2 . When wrapping is near to the infinite 2 ^ N and 2(2N+1) ^ 2 congruent tetrahedron, it is found that there are three methods. http://math.sjtu.edu.cn/Conference/SCAC/slide/HaishengLiang.pdf
标签: Alveolate
