# 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:

 (3,6,3,6) (3,4,6,4) (3,12,12) (3,3,3,4,4) (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.

### Polyominoes

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.