As explained in the previous chapter, the PSOM builds a parameterized associative map. Employing the described class of generalized multi-dimensional Lagrange polynomials as basis functions facilitates the construction of very versatile PSOM mapping manifolds. Resulting unusual characteristics and properties are exposed in this chapter. Several aspects find description: topological order introduces model bias to the PSOM and strongly influences the interpretation of the training data; the influence of non-regularities in the process of sampling the training data is explored; “topological defects” can occur, e.g. if the correspondence of input and output data is mistaken; The use of basis polynomials affects the PSOM extrapolation properties. Furthermore, in some cases the given mapping task faces the best-match procedure with the problem of non-continuities or multiple solutions. Since the visualization of multi-dimensional mappings embedded in even higher dimensional spaces is difficult, the next section illustrates stepwise several PSOM examples. They start with small numbers of nodes.