论文标题
十二面体结构带有mosseri-sadoc瓷砖
Dodecahedral Structures with Mosseri-Sadoc Tiles
论文作者
论文摘要
代表根晶格D6的Delone细胞的3D-FACET，其在交替顺序的六维欧几里得空间的瓷砖被投影到三维空间中。它们分为边缘长度为1和黄金比（tau）的六个摩泽里 - 萨多克四面体瓷砖，面部正常为5倍和3倍轴。二十面体，十二面体和Icosidododecahedron，其顶点是从二十面体群的基本权重以六个四面体而阐述的。一组四个瓷砖由六个基本瓷砖组成，其面与二十面体群的5倍轴正常。结果表明，3D-Euclidean空间可以通过复合瓷砖面对面的面孔面对面，并通过通胀矩阵产生的通胀因子Tau。我们注意到，边缘长度为1和tau的十二面体自然出现在通胀的第二阶和三阶。在充气的十二面体结构中获得了5倍，3倍和2倍对称的3D斑块，其边缘长度tau tau to to n均等3或大于3。复合瓷砖面的平面瓷砖遵循罗宾逊Triangles的边缘到边缘匹配。
3D-facets of the Delone cells representing the deep and shallow holes of the root lattice D6 which tile the six-dimensional Euclidean space in an alternating order are projected into three-dimensional space. They are classified into six Mosseri-Sadoc tetrahedral tiles of edge lengths 1 and golden ratio (tau) with faces normal to the 5-fold and 3-fold axes. The icosahedron, dodecahedron and icosidodecahedron whose vertices are obtained from the fundamental weights of the icosahedral group are dissected in terms of six tetrahedra. A set of four tiles are composed out of six fundamental tiles, faces of which, are normal to the 5-fold axes of the icosahedral group. It is shown that the 3D-Euclidean space can be tiled face-to-face with maximal face coverage by the composite tiles with an inflation factor tau generated by an inflation matrix. We note that dodecahedra with edge lengths of 1 and tau naturally occur already in the second and third order of the inflations. The 3D patches displaying 5-fold, 3-fold and 2-fold symmetries are obtained in the inflated dodecahedral structures with edge lengths tau to the power n with n equals 3 or greater than 3. The planar tiling of the faces of the composite tiles follow the edge-to-edge matching of the Robinson triangles.
