Answer: The history of tessellations dates back to ancient civilizations such as the Egyptians, Greeks, and Romans who used tessellations in their mosaics and geometric designs. The concept of tessellations was formalized by mathematicians such as Albrecht Dürer and Johannes Kepler in the Renaissance period.
There are three main types of tessellations:
Regular Tessellations: These are tessellations made up of congruent (identical) regular polyggon shapes that completely fill the plane without any gaps or overlaps. There are only three regular polyggon shapes that can form regular tessellations: triangles, squares, and hexagons.
Semi-Regular Tessellations: These are tessellations made up of more than one type of regular polygon shape, but still filling the plane without any gaps or overlaps. There are only eight semi-regular tessellations possible, each made up of two or more different types of regular polyggon shapes.
Archimedean Tessellations: These are tessellations made up of two or more types of regular polygon shapes, but with different polygon shapes having different sizes. These tessellations still fill the plane without any gaps or overlaps, but the shapes are not congruent like in regular or semi-regular tessellations.
Step-by-step explanation: