论文标题
二十面体瓷砖与十二面体结构
Icosahedral Tiling with Dodecahedral Structures
论文作者
论文摘要
可以将二十面体和十二面体剖析到来自代表根晶格D_6的深处和浅孔的DeLone多面体的3D-FACET上投射的四面体瓷砖。边缘长度1和τare的四面体的六个基本瓷砖组装成四个复合瓷砖，其脸部正常与二十面体组的5倍轴。 3D欧几里得空间由复合瓷砖面对面，其通胀因子通过通胀矩阵产生了膨胀因子。上的瓷砖是在瓷砖面部的二维中的小管三角形瓷砖的概括。瓷砖的某些组合构成十二面体长度为1，黄金比τ=（1+ \ sqrt（5））/2。
Icosahedron and dodecahedron can be dissected into tetrahedral tiles projected from 3D-facets of the Delone polytopes representing the deep and shallow holes of the root lattice D_6. The six fundamental tiles of tetrahedra of edge lengths 1 and τare assembled into four composite tiles whose faces are normal to the 5-fold axes of the icosahedral group. The 3D Euclidean space is tiled face-to-face by the composite tiles with an inflation factor τgenerated by an inflation matrix. The aperiodic tiling is a generalization of the Tubingen triangular tiling in 2-dimensions for the faces of the tiles are made of Robinson triangles. Certain combinations of the tiles constitute dodecahedra with edge lengths of 1 and the golden ratio τ=(1+\sqrt(5))/2.
