Question

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

Answer 1

To tessellate a regular polygon, the internal angle must be an integral factor of 360. A regular hexagon can tessellate with three corners at a point, the minimum. The internal angles of regular polygons with more than six sides will exceed 120.
In fact, the only regular polygons to tessellate an infinite plane are triangles, squares, and hexagons.