Why is it possible for a regular polygon with more than six sides to tessellate the plane?

Answer 1

A regular polygon is one in which all of the sides and angles are equal. A regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A regular tessellation means a tessellation made up of congruent regular polygons. Vertex is a point at which three or more tiles in a tessellation meet. Two tiles cannot meet in a point, but would have to meet in line. Since the interior angles get larger as the number of sides in a polygon gets larger, no regular polygons with more than six sides can tessellate by themselves. Since the regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees. This works for the triangle, square, and hexagon, and you can show working tessellations for these figures. For all the others, the interior angles are not exact divisors of 360 degrees, and therefore those figures cannot tile the plane.