Penrose tiling contains all six decagons and have a great chence to be extended to infinity and defect free ,Penrose Garden Chung Yuan Kung－貢中元的部落格

Penrose tiling contains all six decagons and have a great chence to be extended to infinity and defect free

世界上第一個包含所有六個不同十邊形的大型彭羅斯瓷磚，並且有很大的機會擴展到無窮大。world first large Penrose tiles that contains all six different decagons, and has a great chance to be expanded to infinity. Be noted first, fig 2,3,4, hide a correctable defect. 如果不考慮上面定義的關於缺陷的限制定義，如果不考慮先前定義的關於缺陷的極端限制性定義，六個十邊形可以共存於彭羅斯瓷磚到無窮大，見最後圖 9 Six decagons can co-exist in a Penrose tiling to infinity if the previously defined extremely restrictive definition of defects is disregarded, see the last figure

This Penrose tile is specially made for demonstrating an extension skill, in fact this one contains five Decagons

這塊彭羅斯牌是專門用來演示擴展技能的，實際上這塊是五個十邊形。as shown in fig 1

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首先，可以製作鏡像耦合，並檢查潛在缺陷的產生 First, mirror couplings can be made and checked for potential defect generation as shown in fig 2 and a type- f decagon engenerated

首先，總是可以製作任何深度的鏡面耦合，但發現潛在缺陷的產生並不是很簡單,, 如霧2所示。這一個可能有機會擴展到無窮大。和一個 f 型十邊形生成

first, any depth of mirror coupling can be always made, but found out a potential defect generation is not quite simple. as shown in fig 2. This one may have chance to be expanded to infinity.

Cut out an appropriate symmetrical area, here a relatively small area is chosen for demonstration. as shown in fig 3. In fact there exists more than one set of so called appropriated symmetry area

剪出一個合適的對稱區域，這裡選擇一個比較小的區域進行演示 3 實際上存在不止一組所謂的適當對稱區域

最後一道工序是做一個五折旋轉鑲嵌，修改接縫區的十邊形。The last process is to make a five fold rotational tessellation , and revised the decagons in the seam zone as shown fig 5. It revealed a tiles

如圖 5 所示。它揭示了一個由所有六個不同的十邊形組成的五角大樓形狀的瓷磚。as shown fig 5. It revealed a Pentagon shape tile consisted of all six different decagons.following the same procedures, it can extend to infinity without generating defect.按照相同的程序，它可以擴展到無窮大而不會產生缺陷 (。