Tiling The Plane
A polygon can tile the plane if congruent copies of the polygon cover the plane without any gaps or overlaps. Which of the following regular polygons can tile the plane?
I. Equilateral Triangle
II. Square
III. Regular Pentagon
IV. Regular Hexagon
Picture Source File: Wikimedia Tesellation
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1 solution
Solution: The image below shows tilings of the plane by equilateral triangles, squares, and regular hexagons. Because the interior angle of a regular pentagon is 108 degrees, pentagons do not fit together to tile the plane.