貢中元的部落格

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.

 When I attend my 50 year anniversary, I asked physics dept to give a speech abot Penrose tiling. Because during Covid 19 mperiod, a  I afraid use public transpotation may have chance to be get influence infection and affect to my 99 year old mother. at that day  I drove my car by myself with a poor  eye seeing. 
at that day I drove my car by myself , I found my poor eye seeing. When I try my transparencies, I found that I can not clear see the images on the screen, and i can not see the red arrow cursormark那一天是在物理系大廳吃大餐前20分鐘的演講，大家應該只想到吃飯，另外一個同學還在當董事長， 說了一句，他弟弟很厲害。

Pseudo chemistry with decagonal tiling and six decagons coexisted without any defect
ABSTRACT