The even-sided polygon p = (IHJFKEMG) is non-symmetric and the orbit s = (LNOYPRST) of an arbitrary point L, with respect to the symmetries on the vertices of p, creates a closed polygon. N is symmetric to L w.r. to H, O is symmetric to N w.r. to J, etc. (The remark, for the general construction with arbitrary parallelogramms on the sides of an n-gon, is due to Antreas Varverakis). For symmetries on the vertices of a general even-sided polygon look at the file: SymmetriesOnVerticesEven.html .