A regular tessellation (tiling a plane edge-to-edge with congruent regular polygons and no gaps) is only possible with regular polygons whose interior angle divides evenly into 360 degrees when polygons meet at a vertex -- this restricts regular tilings to the equilateral triangle (3-gon), square (4-gon), and regular hexagon (6-gon).
For regular polygons to tile a plane with no gaps, an integer number of them must meet exactly at each vertex, i.e., their interior angle...
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