The 3-mirror system reacts similarly to the 2-mirror with one major exception. A third mirror replaces the blackened side of the triangle in the 2-mirror and produces a continuation of reflections throughout the entire field of view. Symmetrical images are much harder to achieve in 3-mirror systems because now there are 3 angles which must be accurate instead of only the one angle in the 2-mirror design.
Again it is important that the mirrors be set at an angle which can be evenly divided into the 360 of the circle; such as 90, which divides into 360 4 times, or:
The other important rule which governs symmetry throughout is that the sum of the 3 angles must total 180 (the total number of degrees in a triangle). Using both these rules, only 3 combinations produce the desired effect. The most common and simplest arrangement is the 60 - 60 - 60 equilateral triangle. Here each angle produces 6 fold patterns which results in a design (FIG3) of continuous triangles.
The second combination is the 45 - 45 - 90 isosceles right triangle. This relationship produces 8 fold patterns at the 45o angles and a 4 fold pattern at the 90 angle, effectively producing continuous square patterns. The sequence of reflections is as above.