Rotation Tessellations

To make a reflection tessellation, you must start with a(n) 60°/120° rhombus. You can create one of these very easily.

Getting Started. . .

1. Place points B and D on the screen. Select B, then D and make a circle by center and point.

2. Next select D, then B and make another circle by center and point.
3. Label the intersections of the two circles A and C.
4. The points A, B, C and D are the four vertices of your rhombus. You don't need to draw in the segments because you're going to have to hide them later anyway.

 

To create the tessellation pattern. . .

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

2. Connect points A and B with some wacky series of curves and segments. (SEE BELOW)

3. Select the vertex point B and mark it as the center, either by double clicking or by using the transform menu.

4. Select the new wacky shape you just created (but not the endpoints A and B) and rotate it around the point B by -120° (or 120° if that doesn't work) . The shape should connect up with the next vertex point C. (SEE BELOW)

5. Next, draw in the diagonal AC and mark it as a mirror, either by double-clicking or by using the transform menu

6. Select the entire shape (but not the diagonal AC and not the vertex points A and B) and reflect it about AC. (SEE BELOW)

7. Hide diagonal AC and then drag the points around until your shape looks cool and none of the lines overlap.

To repeat your pattern to fill the page. . .

1. Choose point B 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 120°.

3. Quick, while everything is still selected, rotate it again by 120°!

4. Choose another point (on the outer edge of the whole shape) that looks like the direct image of point B and mark it as the center. (If you guess wrong, you can always go back using "Edit-Undo").

5. Select everything in the picture (open apple-A is a shortcut) and rotate it by 120°.

6: Quick, while everything is still selected, rotate it again by 120°! Continue steps 4-6 until you have enough shapes. Don't go crazy because you'll overload the memory of the machine!!

Voila!! You have completed the tessellation!!