A turtle geometric construction on the plane, called a polynomial generated polygon (PGP) and represented by Pf,pm, is generated from the sequence obtained from evaluating f(x) ∈ Z[x] over Z modulo pm where p is a prime and m ∈ N. Computational methods are developed to pre-calculate the symmetries exhibited by Pf,pm for a given f and pm. These include procedures to find whether Pf,pm is bounded or unbounded, the degree of rotational symmetry present, whether lines of reflectional symmetry can be observed, and in the case of Pf,pm unbounded, whether the PGP has a glide reflection. Methods are also sought to find a suitable f and pm to produce a desired 'feasible' shape in a PGP construction, and how the same shape might be generated modulo pm+k if it cannot be produced modulo pm.