Tessellations can also be referred to as Euclidean or Non-Euclidean:
EUCLIDIEAN GEOMETRY is the mathematics of flat surfaces.
NON-EUCLIDEAN GEOMETRY is the mathematics of curved surfaces.
Developed in the 19th century, non-euclidean geometry forced mathematicians to understand that curved surfaces have completely different rules and geometric properties compared to flat surfaces.
As an example, a triangle would have different angles and line curvatures in each of the three geometries. So would squares and in fact, so would all shapes.