Tessellation Math Example 1

Solution

1. 1
   For a regular polygon to tessellate alone, its interior angle must divide $360°$ evenly.
2. 2
   Interior angle of a regular hexagon: $\dfrac{(6-2)\times180°}{6} = 120°$. And $360° \div 120° = 3$ (whole number). So exactly $3$ hexagons meet at each vertex. ✓
3. 3
   Interior angle of a regular pentagon: $\dfrac{(5-2)\times180°}{5} = 108°$. And $360° \div 108° = 3.\overline{3}$ (not a whole number). ✗
4. 4
   Since $3.\overline{3}$ pentagons cannot fit exactly around a vertex, regular pentagons do not tessellate.