What are tessellations?
What are tessellations? A tessellation is a series of shapes that cover a plane without any gaps. It could be like the tile in your shower.
This concept was turned into art by M. C. Escher. More background can be found at the related link below.
Non-regular tessellations is a tessellation in which there is no restriction on the order of the polygons around vertices. There is an infinite number of such tessellations. These are tessellations with nonregular simple convex or concave polygons. All triangles and quadrilaterals will tessellate. Some pentagons and hexagons will.
Tessellations of regular polygons can occur only when the external angle of a polygon is equal to a factor of 360. As such, the only tessellations of regular polygons can occur when the internal angles of a polygon are equal to a factor of 360. As such, the only regular polygons which tessellate are triangles, squares, and hexagons.
According to my math textbook tessellations are prominent in Islamic art, Italian mosaics, quilts and ceramics. A very famous tessellation artist is M.C.Escher he created many paints, drawing, and prints using tessellations of interlocking animals. His art reflects the mathematics that underlies all things. Tessellations are frequently used in graphics arts and interior decorating. Since the Koran forbids the use of images of people or animals, many Muslim buildings are decorated with tessellations.