If You Look at a Completed Tessellation, You Will See the Original Motif Repeats in a Pattern

If you look at a completed tessellation, you will see the original motif repeats in a pattern. Two possibilities shown here are in a line facing one way, and then in a line facing the other, or, it may be in a whorl of rotated instances. This is symmetry. There are 17 possible ways that a pattern can be used to tile a flat surface or 'wallpaper' - see the Pólya diagram in Escher section above [click to go there]

There are 4 ways of moving a motif to another position in the pattern. These were described by Escher, and Doris Schattschneider has drawn a diagram, using his creatures, to explain it.

Symmetry is a complex mathematical subject and, as stated earlier, this site is here to encourage the graphical aspect. There are several excellent sites on the Internet which cover the maths side and give graphical examples (see links in site info) and I also recommend 2 books - click next button.

Ninth grade http://www.tessellations.org/tess-reference.htm

A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher. Tessellations are seen throughout art history, from ancient architecture to modern art.

In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics.[1] The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations, often made of glazed clay.

Eighth Grade http://en.wikipedia.org/wiki/Tessellation A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.

Another word for a tessellation is a tiling. Read more here: What is a Tiling?

A dictionary* will tell you that the word "tessellate" means to form or arrange small squares in a checkered or mosaic pattern. The word "tessellate" is derived from the Ionic version of the Greek word "tesseres," which in English means "four." The first tilings were made from square tiles.

A regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A regular tessellation means a tessellation made up of congruent regular polygons. [Remember: Regular means that the sides of the polygon are all the same length. Congruent means that the polygons that you put together are all the same size and shape.

Seventh Grade http://mathforum.org/sum95/suzanne/tess.intro.html

http://www.youtube.com/watch?v=mnFeiWlSKog