Initially four of the r points are all in a straight line, but vertically, in the order (r2, r1, r4, r3) with r0 at the right. This contrast with the order (r1, r3, r2, r4) of the previous example. It is an artefact of the applet that at first the two green lines joining r1 and r4 to the vertex r0 are not drawn. Moving a0 a little bit makes them appear. We see that for small blue radius the green figure is actually convex, for somewhat larger blue radius we have a non-convex pentagon and for large enough blue radius we have a reentrant pentagon.The theory of the Discrete Fourier Transform of order 5, i.e., harmonic analysis in the cyclic group of order 5, a.k.a. the basic Geometric Fourier Transform that takes arbitrary pentagons to their equilateral and anti-equilateral harmonic components tells us that any pentagon can be constructed in the way the mechanism here illustrates, provided its center of gravity is at the origin. That is constructed by taking a standard equilateral pentagon with positive orientation, rotating and dilating it (bigger or smaller), doing the same with the reverse orientation and with pentagrams and averaging four suitable parts.