Tessellations: tiling a flat surface · Pulse Beat
A tessellation covers a flat surface with shapes and no gaps or overlaps. Only three regular polygons can do it on their own: equilateral triangles, squares and regular hexagons.
A tessellation covers a flat surface with shapes and no gaps or overlaps. Only three regular polygons can do it on their own: equilateral triangles, squares and regular hexagons.
The reason is angles. At each point where tiles meet, the angles must add up to 360°. Triangles have 60°, so six meet (6 × 60 = 360). Squares have 90°, so four meet. Hexagons have 120°, so three meet. A regular pentagon has 108°, and 360 isn't a whole number of 108s, so pentagons leave gaps.
Bees choose the hexagon for honeycomb. Among these three shapes, a hexagon encloses the most area for the least wall.
Any triangle and any four-sided shape can tessellate too, and artists like M. C. Escher bent such shapes into birds and lizards.