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Mathematics

Tessellations and the Classification of Regular Tilings

Quick fact

Only three regular polygons can tile the entire plane without gaps or overlaps: equilateral triangles, squares, and regular hexagons. This surprising limitation arises directly from the requirement that the interior angles around a vertex must sum to exactly 360°.

Why this is interesting

You've seen hexagonal tiles in bathrooms and square grids on graph paper, but have you ever wondered why you never see a regular pentagon tiling a floor? What's so special about the shapes that can tile a plane perfectly?