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They tessellate because one of their interior angles is exactly 120 degrees provided that it is a regular polygon. Since this is exactly a third of a full circle, three of them will always create a 360 degree angle in the center. When you repeat this pattern, they form multiple 360 degree angles, which forms a tessellation. This is true with any polygon that has an interior angle that is a factor of 360, and this is why pentagons do not tessellate.

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10y ago

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