Tilings in a hexagonal grid

In my paper, I will research on tilings in more complicated geometry, a hexagonal grid. Denote the n-set as {p1, p2, …, pn}, where pi is a point on the hexagon grid. Any set, which is obtained by an n-set via reflection, translation and rotation, is considered as its congruent set. We will examine whether a random n-set, where n is 2, 3, or 4, and its congruent sets can tile a whole infinite hexagonal grid. If not, we will figure out whether there exist some specific geometries of the n-set that enable it and its congruent sets to tie a whole infinite hexagonal grid. Understanding symmetry and tilings in hexagonal grid will provide people with insights in different scientific fields. For example, R. Twarock developed a tiling approach, by studying tilings in virus capsid, to predict the formations and types of some virus, like polyoma virus, whose structure cannot be fully explained by other theories.

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