貢中元的部落格

所有十邊形彭羅斯瓷磚 

Celebrating the 50th anniversary of the discovery of Penrose tiling

The five-fold symmetrical tile that can be self-coupled to build up a five-fold tiling,periodic and four-way symmetry tiles (crystals) to infinity

Some smaller unit cells that form different decagonal two-dimensional crystals

Four unit cells that intercepted from a translational decagonal style crystal and form four different crystals.

Tessellation of unlimited equilateral rhombuses

 If the acute angle of a rhombus is 90/N degrees, and N is an integer, then there can be N equilateral rhombuses whose acute angles are integer multiples of 90/N respectively. A standard drawing method with numerous variables, in which N equilateral rhombus can be tessellated into an infinite number of groups (kinds) of combinations of infinite pattern. There are four general rules of drawing, which are described hereafter.

new

tellation of three triangles

asymmetry  Penrose binary  tiling  不對稱彭羅斯平鋪 

1 one may start from any conventionally defined five-fold symmtry (around a specific center, center of blue star,)or on-five fold symmerric  penrose tile , either pentagonal or circular shape.as shown in fig 1

All  aperoidic and periodicPenrose (Kung)  tiling  (# one set全集之2)

All  Penrose kung tiling 

石 ​​我從頭從原子,分子的觀念來闡述胖瘦二種菱形形成六種正十角形(類分子)、然後再用六種正十角形,以高分子簇(Clusters)的概念規範了幾類五邊形(像Penrose tiles)的簇類,同時也定義了在簇裡面缺陷的含義,,,再利用群簇耦合的概念,耦合的簇邊界的分子轉換製繪無限大的 defect free Penrose鋪磚圖,,,,,這種邊界化學概念的反應有助於了解五重性合金quasicrystal準晶体的曉解.