What is Tessellation?

I thought before continuing to post any further tessellations it's worth writing a little about Tessellations:

Tessellation is when a shape or a pattern is repeated over a plane without leaving a gap between any patterns and with no overlapping. Tessellation is also called tiling.Honeycomb is an example for tessellation in nature.

Another simple example of tessellation is floor tiles. Square tiles repeating with no gaps (Figure 1). This is an example for regular tessellation. Spread hexagons is an example of regular tessellation. There can be only three possible regular tessellations with repeating Squares, triangles and hexagons.

The other type is semi-regular tessellation or Archimedean tessellation. This type of tessellation contains two or more different regular polygons. Example, a tessellation with repeating hexagons surrounded by triangles (Figure 2).

Naming convention: A tessellation is named after the polygons it contains. If there are repeating squares, it is named as 4.4.4.4, considering a vertex, and polygons that surrounds this vertex. 4.4.4.4 is an example of regular tessellation.

A semi regular tessellation for example one which has hexagons and triangles are named as 3.6.3.6. The smaller polygon is mentioned first while naming. For example, for the below semi regular tessellation the naming cannot be 6.3.6.3.

Figure 1

Figure 2

Tessellation techniques are widely used in computer graphic designs. One example is it's application in nvidia's DirectX 11. It is used in GTX 400 series GPUs to improve performance. A much detailed and interesting article about the nvidia product and how tessellation feature is used to enhance the performance is provided in their website:

http://www.nvidia.com/object/tessellation.html

Source and reference:

http://mathforum.org/sum95/suzanne/whattess.html

Related links and further reading:

http://www.mathsisfun.com/geometry/tessellation.html

http://www.coolmath4kids.com/tesspag1.html

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

http://www.csun.edu/~lmp99402/Math_Art/Tesselations/tesselations.html