Explain why not all regular polygons will tessellate. 10 points?

A regular polygon will tessellate (the plane) if and only if the measure of an interior angle evenly divides 360 or equivalently (n - 2) | 2n. And if (n - 2) | 2n, then (n - 2) must also divide (2n) - 2*(n - 2) which equals 4. Therefore, n = 3, 4, or 6. We see that only an equilateral triangle (n = 3), a square (n = 4), or a regular hexagon (n = 6) will tessellate. All other regular polygons will not.