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Identifying the points corresponding to parity conditions satisfying m, n, p and q with associated pentagons and pentagonal networks for a range-1, b range-2 and c range-3
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Parity conditions, a property of the generalized coordinates of two dimensional Penrose tilings, as deduced by Ramachandrarao et al. while proposing a geometrical algorithm, have been analyzed independently to understand their role in the generation of Penrose tiling. Our objective has been to establish the physical significance of these conditions...
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... parity conditions only. However, if we adopt a rule of joining the points together through the lines parallel to a regular pentagon, it was noticed that most of the points can be connected with each other through regular penta- gons, except for the range-1, where we have two isolated pentagons, consuming 10 points out of 15 generated points (Fig. 2a). However, for range-2 and range-3, we generate a network of inter connected pentagons of equal edge length, where all the vertices of pentagon are occupied by a parity condition satisfying points, leaving some points unoccu- pied (Fig. 2b, c). Although, a selective group of parity conditions satisfying points does show their possible ...
Context 2
... except for the range-1, where we have two isolated pentagons, consuming 10 points out of 15 generated points (Fig. 2a). However, for range-2 and range-3, we generate a network of inter connected pentagons of equal edge length, where all the vertices of pentagon are occupied by a parity condition satisfying points, leaving some points unoccu- pied (Fig. 2b, c). Although, a selective group of parity conditions satisfying points does show their possible cor- relation with two dimensional lattices having pentagonal building unit (as shown above), it does not ensure a fivefold rotational symmetry for the pattern. We have also tried to cover the two dimensional space as created by parity ...
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