Once a prime number has been chosen for the number of vertices, the circle must be divided into that many equal divisions. This is done with the dividers, or a compass, and is the most critical step in drawing an accurate template. Start by calculating the distance between points by dividing the circumference of your circle by the number of vertices you desire. Set the distance of your dividers to equal this distance and walk them around the circle. Walking the dividers set at this calculated distance around the circle will tell you how close your initial setting is to the exact one. Ideally, traveling once around the circle should bring the point of the dividers right back to the first mark. This rarely happens on the first trial, but repeated adjustments of the divider setting will lead eventually to an equidistannt set of points,
The circumference "C" of a circle with radius r is given by
C = 2 pie r~ 6.3r.
When the correct setting is found, each indicated point should be marked on the template, as shown above. Check to make sure the total number of marks is equal to the number expected! It's easy to leave one out or add one extra without noticing. After the divisions are marked and double checked, the template is finished.
 

The theory of threading a Mandala geometric thread design is simpler than most people realize.
Basically, the threading of each layer involves nothing more than counting a certain number of points between connected points. In the design being started in the picture above, there are 53 brass pins located at the vertices.
Of the (53 - 1)/2 = 26 possible circular layers, that one which results in the second smallest circle is being started. Thus after tying the thread at an arbitrary starting point, it is wound around the 25th pin (counting clockwise). Counting in the same direction another 25 pins brings the thread to the next point to be connected, and this process is continued until all the pins have been connected and the first layer is completed. This brings the thread back to the starting point where it is tied off.
 

Opening Lissajou