Step 1:

Draw a perfect circle. Choose a whole number for it’s diameter, e.g. 27 pt. Calculate the circumference of the circle. The circumference is the diameter times pi (d * PI). Note this number. (e.g. 27 * PI = 84.823)

Step 2:

Draw the shape that you want to tile radially, for example, the shape shown below:

Place this shape so that the part that you want to connect is even with the circle from step one, like this:

The red dotted line segment shows the length that we are concerned with for this step. Take the circumference of the circle from step 1, and divide it be an integer. This integer could be any whole number, and it is equal to the number of times you want to tile the shape.  For instance, in this example we’ll use 34 as our integer, so 84.823 / 34 = 2.495, so we want to make the length indicated by the red dotted line segment to equal 2.495.

Step 3:

Now we need to find the rotation for each repetition.  Basically, this is just 360º divided by the integer from the last step.  So in our example, we’ll use 360º / 34 = 10.588º.

Step 4:

Copy the shape from step 2, rotate it 180º, and place them so that the red-dotted line segment lines up with opposite sides of the circle and justify everything center.  Select both of them and copy paste and rotate the number from step 3 (10.588º), then copy, paste in place, repeat (cmmd-C, cmmd-F, cmmd-D) for half of the number of times in step 2. (e.g. 34 / 2 = 17)

Have fun!

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Quick Tutorial: Radial Repeat