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
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1 solution
Solution: The image below shows tilings using equilateral triangles, squares, and regular hexagons. Because the interior angle of a regular pentagon is 108^\deg , pentagons do not fit together to tile the plane.