Axis of quinary symmetry occur in molecular symmetry, as in the case of fullerenes, and in crystalline symmetry, in the quasicrystals. Minerals with pentagonal faces do not have this element of symmetry, as the pyrite (FeS2) which shows a ridge that is different from the other ones, in any face of the crystal. The purpose of this paper is to demonstrate conceptual differences between pyritohedron and regular pentagonal dodecahedron symmetries, discussing students' difficulties to identify them. Also is proposed a didactic experiment with spatial models of the above-mentioned forms and the demonstration of its symmetries in clinographic projections.