A tessellation is when a shape is repeated over and over, covering a plane without any gaps. In a Euclidean plane, triangles, squares, and hexagons are the only regular polygons that can tessellate.
This is because if you find the interior angle of a polygon, the angle measure must be a divisor of 360 degrees in order for the tessellation to occur without any gaps in-between. You can find the interior angle measure of a polygon by taking the total interior angle measure (ex: 180 degrees for a triangle, 540 degrees for a pentagon, etc..) and dividing that number by the number of sides the polygon has. If this number is a divisor of 360, then it is a regular tessellation. Interestingly, only triangles, squares, and hexagons produce these types of numbers- which is part of what makes them such unique and interesting shapes!
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