How you know when a pattern of shapes forms a tessellation?

Question

How you know when a pattern of shapes forms a tessellation?

Answer 1

As I understand it, only certain shapes can form a simple tessellation by themselves. There are combinations of shapes that form complex tessellations. From the website link below:

"The only regular polygons which will tile by themselves are triangles, squares, and hexagons. If different types of regular polygons are used together, however, other types of polygons will tessellate."

The website will provide you a great bunch of resources...good luck!

Answer 2

Here's some info I gathered before about making tessellations that should be helpful:

tessellation:

a closed shape or polygon that repeats on all sides without leaving any gaps

. . Start with a parallelogram (square or rectangle), then  modify opposite sides in exactly the same way, to create an interlocking pattern.  (In other words)...add to the bottom the area that was taken from the top, and to the left side add the area taken from the right side. The resulting piece is a fundamental region which will fit with itself to fill the plane without gaps or overlaps...."  and tessellate

And similarly:

tessellations . . I have been absorbing a great book-Designing Tessellations, by Jinny Beyer. If you have ever looked at an M.C. Escher print and wondered how he made his facinating interlocking patterns, now you can learn how! It seems so simple when someone shows the steps.

... Basically, you take a standard shape, like a square, and carve out a piece, then place that piece on another side of the square facing out. Now you have a basic shape that will interlock with itself! You can carve some more from another side and add that to a different side, and still have a "tile" which will interlock with itself to form bazillions of designs!

...The book shows detailed ways to use the same pattern, like cane slices, and put them together in 17 symmetrical ways. This may be old news to some, but for me it was a great revelation! I got into this because I have been translating quilt patterns into clay... I was amazed at how many different designs could be made with the same basic block or "tile". Crafty Fox

http://www.cs.unc.edu/~davemc/Pic/Escher... (Escher tessellations, etc.)

...Escher (reflection and translation symmetry)

http://www.dartmouth.edu/~matc/math5.pat...

http://www.dartmouth.edu/~matc/math5.pat...

http://www.geocities.com/williamwchow/ja... (many, many examples, plus info)

HTH,

Diane B.