A two-mirror kaleidoscope can be made with only two front (or first) surfaced mirrors. This configuration produces an entirely different pattern when viewed. Above is a picture from a cellscope using only two mirrors. Notice that the image is somewhat round. However, closer inspection will show that the image contains a 5-point star. And herein lies the science.
By varying the angle between the two mirrors, any number of star points are achievable. Great patience must be taken when assembling 2-mirror systems to ensure that there is an exact number of points. The mirrors are adjusted while looking through the scope until the desired pattern is obtained. When the angle of the mirrors does not produce a whole number, the image will not be satisfactory. For example, a 5-1/2 point star would not be cool. This is one of those things that one is probably better off seeing demonstrated rather than trying to figure it out for yourself.