I don`t wanna dance alone.

Patricia Armamento II-3

1) A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of 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, who was inspired by studying the Moorish use of symmetry in the Alhambra tiles during a visit in 1922. 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.

http://en.wikipedia.org/wiki/Tessellation

2) REGULAR TESSELLATIONS:

RULE #1:   The tessellation must tile a floor (that goes on forever) with no overlapping or gaps.

RULE #2:  The tiles must be regular polygons - and all the same.

RULE #3:   Each vertex must look the same.

SEMI-REGULAR TESSELLATIONS:

These tessellations are made by using two or more different regular polygons. The rules are still the same. Every vertex must have the exact same configuration.

3) Examples:

Regular Tessellations: 

Semi-regular Tessellations: