What kinds of regular polygons can be used for regular tesselations

A. Six-sided

B. Five sided

C. Three-sided

D. Four-sided

To tessellate a surface using a regular polygon, the interior angle must be a sub-multiple (i. e. factor) of 360 degrees to cover completely the surface.

For a regular three-sided polygon, the interior angle is (180-360/3) = 60 °

Since 6*60=360, so a regular three-sided polygon (equilateral triangle) tessellates.

For a regular four-sided polygon, the interior angle is (180-360/4) = 90 °

Since 4*90=360, so a regular four-sided polygon (square) tessellates.

For a regular five-sided polygon, the interior angle is (180-360/5) = 108 °

Since 360/108=3.33 ... (not an integer), so a regular five-sided polygon (pentagon) does NOT tessellate.

For a regular six-sided polygon, the interior angle is (180-360/6) = 120 °

Since 3*120=360, so a regular six-sided polygon (hexagon) tessellates.