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Tessellations - M. C. Escher and how to make your own Tessellation Art

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Escher-style tessellation art, with only easy geometry: Do-it-yourself lessons and projects, art galleries, history, & contests.

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A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.

Examples:

Rectangles

Octagons and Squares

Different Pentagons

Regular Tessellations

A regular tessellation is a pattern made by repeating a regular polygon.
There are only 3 regular tessellations:
Look at a Vertex ...

A vertex is just a "corner point".

What shapes meet here?

For a regular tessellation, the pattern is identical at each vertex!

Semi-regular Tessellations

A semi-regular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same!
There are only 8 semi-regular tessellations:

Question 1: For all the tessellations above, is the pattern the same at each vertex?

Question 2: One of those patterns becomes different when we make a mirror-image of it ... which one?

Other Tessellations

There are also "demiregular" tessellations, but mathematicians disagree on what they actually are!

And some people allow curved shapes (not just polygons) so we can have tessellations like these:

Curvy Shapes

Tessellation Artist

All these images were made using Tessellation Artist, with some color added using a paint program.

You can try it too - maybe you will invent a new tessellation!

World Tessellation Day

World Tessellation Day is June 17. Celebrate!

5482, 5483, 5484, 5485, 5486, 853, 854, 3368, 3369, 5487

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Learn how a pattern of shapes that fit perfectly together make a tessellation (tiling)

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Tessellation Artist

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Instructions

First - just play with it! Draw on it. Try the different tools and see what happens.

Tiling Directions

You can control the spacing:

Blue dot controls x-y spacing of grid

Red dot controls rotation of the grid

Best to just try dragging the dots to see what happens!

Polygons

You can draw regular polygons using the polygon tool. Choose the number of sides, from 3 ( Triangles) to 12 ( Dodecagons). You may also need to adjust the angle to get the desired effect.

Nudge and Undo

You can nudge the most recent addition by using the up down left right keys.
Press ctrl to make smaller adjustments.

You can also use "Undo" to remove the last shape.

What Can You Make?

You can make all kinds of interesting patterns! Have a look at the Tessellation page - there are lots of examples of tiling patterns that were made using tessellation artist (some color was added using a simple paint program).

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First - just play with it! Draw on it. Try the different tools and see what happens. You can control the spacing: Blue dot controls x-y spacing of grid Red dot controls rotation of the grid Best to just try dragging the dots to see what happens!

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Yellow, Green or Purple Qs