Hexagons
Yay! Each vertex looks the same - has the exact same composition
of shapes around it:
three hexagons.
The interior angle of a hexagon is 120 degrees.
120 + 120 + 120
= 360 .
Therefore, hexagons tessellate!
Neither do
Octagons
or Nonagons
or Decagons
or in fact, any regular polygon with more than six sides.
They will all overlap and therefore, will not tessellate.
Heptagons
Oh no! The heptagons are overlapping!
There are three heptagons at the vertex.
The interior angle of a heptagon is 128.57 degrees.
128.57 + 128.57 + 128.57
= 385.71.
Not 360!
Therefore, heptagons do not tessellate.