Mr. Kuehl's Tessellation Home Page

The following links will take you to various pages that will teach you about tessellations and in making your own Escher-type tessellations.  There are also pages of sample tessellations grouped by the different types of tessellations, so you can see some finished tessellations of the type you are trying to make.  All of these materials have been developed by Mr. Kuehl and his students and friends.  You are free to use these materials to teach yourself or others about tessellations in non-profit scenarios.  If you reference this material for a paper or workshop, please give Mr. Kuehl proper credit.  Thank you!

For Teachers: Investigating Tessellations Group Activity
This is a four day unit that can be used at many grade levels to have students investigate and create tessellations.  Non-teachers can read through it to learn a number of things about tessellations and how to make them.
You can also download an AppleWorks 6.0 or Word 2000 version below.

Download: AppleWorks 6.0 version
(Click and Choose Save as ...)
Download: Word 2000 version
(Click and Choose Save as ...)
Transparency Template - The following directions on creating Escher-type tessellations by hand assume you have photocopied these templates of figures onto transparency sheets and cut them out along the lines.  Using overhead sheets makes tracing, translating, rotating, and reflecting very easy, and also allows you to correct errors easily.  The sheets are reusable too! (You will need an overhead pen however!) Use one figure to design your piece, and use the other to help you make copies that you can flip, rotate, translate, etc. Overhead Template 1
Overhead Template 2
Overhead Template 3

Making Tessellations by Hand

Escher-type Tessellations by Translation Directions Completed Examples
Escher-type Tessellations by Rotation Around Midpoints of Sides Directions Completed Examples
Escher-type Tessellations by Rotation Around Midpoints of Sides and Translation Directions Completed Examples
Escher-type Tessellations by Rotation Around Vertices Directions Completed Examples
Escher-type Tessellations by Rotation Around Midpoints of a Side and a Vertex Directions Completed Examples
Escher-type Tessellations by Reflection Using a Rectangle Directions Completed Examples
Escher-type Tessellations by Reflection Using a 120 degree Isosceles Triangle Directions Completed Examples
Escher-type Tessellations by Glide Reflection Directions Completed Examples

Making Tessellations by Computer

Note: These directions were created years ago for a workshop at the Wisconsin Mathematics Council's Green Lake Conference.  They are written to be used with ClarisWorks 2.0, but should work for any version of ClarisWorks (now called AppleWorks).  The directions should also be close to what needs to be done for any IBM-based painting program.  Please see the Introduction to the following directions first.
Escher-type Tessellations by Translation Directions Completed Examples
Escher-type Tessellations by Rotation and Reflection
(Using a 120 Degree Isosceles Triangle)
Directions Completed Examples
Escher-type Tessellations by Glide Reflection Directions Completed Examples
Escher-type Tessellations by Rotation Around Vertices Directions Completed Examples

Special Tessellations

Cube Tessellation Directions Completed Examples
Pyramid Tessellation Directions Completed Examples
Kaleidocycle 1 Directions Completed Examples
Kaleidocycle 2 Directions Completed Examples
Static Chain Tessellation Directions Completed Examples
Changing Chain Tessellation Directions Completed Examples