Tessellation Project Today we will discuss the requirements and expectations for your Tessellation projects and you will receive a brief introduction to the different types of tessellations. This is an individual project.

Tessellation Project Maurits Cornelis Escher (1898 – 1972) was a Dutch artist famous for his repetitive, interlocking pattern. His works look like paintings but were done by woodcarving and lithographs. Escher’s designs are made from variations on tiling patterns called tessellations. A floor covered by square tiles is an example of a tessellation of squares.

Examples of M.C. Escher’s Work

Examples of M.C. Escher’s Work

Examples of M.C. Escher’s Work

Examples of M.C. Escher’s Work

Examples of M.C. Escher’s Work

Examples of M.C. Escher’s Work

Tessellations & Transformations Tessellations can be modified by using transformations. As you know, transformations are movements of geometric figures. One transformation, commonly used to create tessellations is a slide, or translation, of a figure.

Translation Tessellations For simple translation tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms.

Example: Translation Tessellation You can create more complex designs starting with square tessellations and making changes on both pairs of sides.

Depending how you decide to color your tessellation, a very simple design can have a very creative result.

Glide Reflection Tessellation For glide reflection tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms.

Example By reflecting and gliding over more than one side, you can create a more complex tessellation.

Adding coloring and features will enhance the artwork.

Tessellation created by Rotation Adjacent sides must be congruent – squares, equilateral triangles, regular hexagons, rhombi

Midpoint Rotations Triangles, Squares, and Quadrilaterals Note: More than one side may be altered for more challenging designs. Coloring one side of the pattern will help prevent accidental flipping during tracing.

Example: Rotational Tessellation

Suggestions Polygons that tessellate include regular triangles, hexagons and any quadrilateral (see images below). It will be easiest to perform transformations (for level 2 and above) on regular polygons like the ones below.

Suggestions A template that is approximately 2 inches by 2 inches will work well to create an 8 ½ by 11 inch tessellation. Try out several designs, by cutting and taping paper together until you find something you like. When you have decided on a design, create your template on cardstock. This is due with the project. Be creative. Your design should not look like any of the designs in this presentation. Remember: Finding a design online and copying it is plagiarism and grounds for a zero.

Tessellation Project You will have time in class to work on this project. The due date will be posted. This assignment is worth a quiz grade. All required materials will be provided, however you can use your own materials if you prefer. Consult the rubric (posted in class) to verify what is required for the project at each level. Use your class time wisely. It will be obvious if you rushed to complete the project at the last minute. The teacher has the right to drop you one or more levels if your participation and/or work quality is not satisfactory.