A variety of equilateral rhombuses can be tessellated into an infinite (non periodic) two-dimensional plane.(ref 1, 二維鑲嵌作圖及錯覺圖案製作 two-dimensional tessellation art and illusion pattern,作者貢中元,Chung Yuan Kung,鴻林圖書有限公司 Honglin Books Co., Ltd. 2021 July), Least elements, minimal variables, (infinite) unlimited combinations, unbounded expansiion (derivatives), of this kind drawing rule is worth demonstrating in further detail.
Rhombus close-packed patterns are observed in nature, for example, the stripes of snail shells and the spiral core-like distribution of sun flower seeds. If we can systematically understand all the possibilities of the rhombus tessellation pattern, it can be helpful to understand the taxonomic details of the similarities and differences of biological growth.
Here explains a standard drawing process that an unlimited number of equilateral rhombuses can be tessellated and extended with an unlimited number of combinations, orderly. . 
If the acute angle of a rhombus is 90/N degrees, and N is an integer, then there can be N equilateral rhombus, whose acute angles are integer multiples of 90/N respectively. So that , a crescent shape can be densely tiled in the sequence of acute angles. N can be 1, 2, 3, 4, 5, to infinity, 90/N can be endless decimals. Then N equilateral rhombuses that have an acute angle of an integer multiple of 90/N degrees, can be sequentially close packed in to a moon like shape with 4N corners and 4N edges with the same length. The case where N is equal to 5 is used here for the convenience of illustration. As shown in Figure 1a, such a crescent-shaped has 2 acute angles of 18 degrees and 18 obtuseside angles of 162 degrees, and 20 angular sides of the same length. Acute angle of 18, 36, 54, 72, 90 rhombuses can be inlaid tightly in sequence, (acute angle difference is 90/N, 18 degrees) .The smallest acute angle and all edge obtuse corner angles of the crescents will be added up to a 180 degrees.
fig 1 This crescent shape has 2 acute angles (18degrees) and 18 obtuse corners (162 degrees), and 20 equal edge length
Two or more crescent shapes can be rotated relatively by an integer multiples of the smallest acute angle 18 degrees (90/5) and fit each other together to form a variety of sickle-shape (鐮刀狀) configurations as shown in the figure 2. In this way, a crescent shape, (with 4N corners and 4N corners), by paralling the different equilateral rhombuses in the sequential of acute angle size , densely tessellated. The crescent shape can be tessellated into different sickle shapes, and then next combined into an infinite spiral pattern.
figure 2 sickle-shape configurations
These sickle-shape configurations can be further combined into specific (mosaic) convoluted ring. pattern, as shown in Figure 3 There are different kind of polygonal in the convoluted ring.
fig3 convoluted ring (with unpacked polygonal core)
In this second way, some diamonds can be combined into simple polygons first, and then combined into large polygons (the obtuse angle is an integer multiple of 90/N), and then expanded (derived) into unlimited final patterns.
fig 4. configuration of polygonal core
Parallel in the same direction
This is simplest way, the rhombus can be arranged in any parallel in the same direction, and then repeat itself in parallel and tessellated to become infinitely patterns. For the case N is lager than 1, semi-symetric tessellation for unlimited number of equilateral rhombuses with an unlimited combinations, can be closely paved orderly . Again, using N is five for example , as shown in Fig 5 . But it seems not easy (but can be) to make an four fold symetric tessellation for N is larger than 4. .
fig 5 , example of semi-symetric tessellation
fig 6 spiral core and first ring
The second way, some diamonds can be combined into simple polygons first, and then combined into large polygons (the obtuse angle is an integer multiple of 90/N), and then derived into infinite patterns. The third way, In the sequential of acute angle size, densely tessellated into a crescent shape, (with 4N corners and 4N corners) a basic cresent shape. The cresent shape can be tessellated into different sickle shapes, and next into an ublimited spiral pattern.
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