Rotation Tessellations

To make a rotation tessellation, you must start with a regular hexagon, a square, or an equilateral triangle.

Follow this diagram for equilateral triangle!! 

 1. Draw two points on the screen and select them both.

2. Open a script that will draw the polygon that you have chosen.

3. Hide the colored interior of the figure as well as the center.

4. Change the color you're working in so you don't lose track of the original vertices.

To create the tessellation pattern:

Follow this diagram for square!!  

 1. Connect the first two vertices, A and B, with some series of segments and curves.

2. Choose point B and use the Transform menu to mark it as the center.

3. Select all the points, curves and segments of your newly created curve (except for points A and B) and uses the Transform menu to rotate them by -120° (or 120°) about point B.

4. (follow the appropriate directions) TRIANGLE: Make a midpoint on the one remaining side of the triangle. Then connect the midpoint to one of the two adjacent vertices with some wacky shape. Select the midpoint as the center and rotate your new curve about the midpoint by 180° (so it matches up with the vertex on the other side.
SQUARE: Repeat steps 2 and 3 on the remaining two sides of the square.
HEXAGON: Repeat steps 2 and 3 twice, once on each remaining pair of adjacent sides.
 
5. Click on each of the labeled vertices with the hand tool to hide the labels of all the points.

 

To create the tessellation pattern:

Follow this diagram for regular hexagon!!  

 1. Choose any vertex of the original figure and mark it as the center using the Transform menu.

2. Select the entire figure (draw a box around it using the arrow tool) and use the Transform menu to rotate it by either 60°(triangle), 90° (square), or 120° (hexagon).

3. Quick, while everything is selected, rotate it again by the same amount. Repeat until that vertex is completely surrounded. (Total of 3 images for triangles, 4 for squares, and 6 for hexagons.

4. Choose a point on the edge that looks like it used to be a vertex of the original shape and mark it as the center.

5. Select the entire figure and rotate it by the same amount as in #2.

6. Quick, while every thing is still selected, rotate it again!

7. When you are completely satisfied with your tessellation, choose the point tool and then go to Edit--Select all points. Then use the display menu to hide all the points. This will make your tessellation look neater.

Congratulations! You've finished your rotation tessellation.