There are an infinite numberof regular polygons, though as the number of sides increases, the polygon begins to look more and more like a circle.
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They are known as regular polygons.
Tessellations
Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation.
no.
Yes, the corresponding sides of two similar regular polygons must have equal lengths. This is because both the polygons are similar, which means that since they are also polygons, they must have equal lengths.