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Unit Cells (2/2)
 

1. Introduction 2. Unit Squares 3. Unit Triangles 4. Unit Hexagons 5. Hands-On Activities
Unit Triangles
Recall that in order to get a successful tiling, the points on the boundaries must line up. So, if the only points on a triangle lie at the vertices, then we can rotate the triangle around one of its vertices to form a regular hexagon. This hexagon can then be easily duplicated to create a tiling.

Example (animated)

See how a "unit triangle" can create a hexagon that can be easily tessellated
Example Tiling

The tessellation that results when the hexagon shown at the left is repeated. The red lines indicate the original pattern.

 

Here is another example of this technique of rotations:

Example (animated)

The original "unit triangle" is indicated by dotted lines. The red lines indicate the hexagon pattern created from rotating the "unit triangle."
Example Tiling

This tiling is a colored version without shape outlines of the tessellation on the left

 

1. Introduction 2. Unit Squares 3. Unit Triangles 4. Unit Hexagons 5. Hands-On Activities
Unit Hexagons
Consider a regular hexagon. What should we keep in mind when drawing a pattern so that the points on adjacent sides will line up? First of all, let's see which sides line up:

Tiling of Regular Hexagons

In a tiling of regular hexagons, opposite sides line up. In other words, sides 1 and 4 line up, sides 2 and 5 line up, and sides 3 and 6 line up.

As you can see, opposite sides of a regular hexagon become adjacent sides in a tiling of regular hexagons. A technique becomes clear: when drawing the pattern inside of the hexagon, make sure that every point on a side has a corresponding point on the opposite side of the hexagon.

Example of Unit Hexagon Tiling

The red, green, and blue dots on the left indicate points which correspond and line up when the hexagon is duplicated. The resulting tiling is shown on the right.

 

Here is another example of this technique. In this example, the only points on the boundaries of the original unit hexagon lie at the vertices of the hexagon. Notice that the pattern is formed by making five copies of a hook-shaped line as it is rotated around the center of the hexagon.

Example of Unit Hexagon Tiling

The white lines on the right indicate the original pattern from the unit hexagon.

 

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Real examples of the unit cells technique:


TemplatesYou can find templates of squares, equilateral triangles, and equilateral hexagons at the templates page. Use these templates as a basis for creating new tessellations with the unit cells technique.

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