Sketches for the Art Project Exploration

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Objective: Practice several of the techniques that will create an Escher-like tessellation.

Using Translations

We have seen before that we can modify geometric tessellations to create tessellations by recognizable figures. We did several in Escher-Like Tessellations Explorations.

Using Rotations

We can rotate about the center of a side or about a vertex.

1. Create some tessellations with 2-fold, 3-fold and 4-fold rotational symmetry. Which ones are easiest to do? What geometric tessellation(s) should you start with in each case?

Using Reflections

Starting with a tessellation by squares or rectangles we can create tessellations with reflectional symmetry.

2. Create some tessellations with reflectional symmetry.

Using Glide-Reflections

3. Starting with a tessellation by squares or rectangles create tessellations using glide reflections.

Using Other Geometric Tessellations

Semi-Regular Tessellations

Recall the Archimedean tessellations:

Archimedean Tessellations
Archimedean3636.svg Archimedean3464.svg Archimedean31212.svg Archimedean33344.svg
(3,6,3,6) (3,4,6,4) (3,12,12) (3,3,3,4,4)
Archimedean488.svg Archimedean33434.svg Archimedean4612.svg Archimedean33336.svg
(4,8,8) (3,3,4,3,4) (4,6,12) (3,3,3,3,6)

4. Experiment with these geometric tessellations and create patterns with recognizable figures from them. Think about which symmetries you want. You can just use translation, or maybe rotations and / or reflections.


5. Start with a tessellation by either a tetromino or a pentomino and create a tessellation by recognizable figures from it. Use a tessellation by an interesting polyomino (i.e. not one of the rectangular ones).

The Art Project

Develop 10 to 15 sketches of tessellations by recognizable figures using several of the above mentioned techniques.