WHAT IS CLAIMED IS: 1. A polyurethane polymer having a density of at least 750 kg/m$^{3}$that is the reaction product of reactants that comprise: a) at least one organic polyisocyanate and b) polyols comprising b-1) one or more polyols having a hydroxyl equivalent weight of greater than 250 g/mol and a nominal hydroxyl functionality of 2 to 4 and b-2) one or more polyols having a hydroxyl equivalent weight of up to 250, wherein at least 50% by weight of b-2) is at least one alkoxylated Mannich base has an average hydroxyl functionality of 3 to 7; wherein the hard segment content of the polyurethane polymer is 20 to 80% by weight of the polyurethane polymer. 2. The polyurethane polymer of claim 1 wherein the alkoxylated Mannich base is represented by the structure: wherein each R is independently hydrogen, linear or branched alkyl having 1 to 18 carbon atoms or linear or branched alkenyl having 1 to 18 carbon atoms, m is a number from 0 to 2, each R$^{1}$is independently hydrogen or linear or branched alkyl having 1 to 6 carbon atoms, each n is a number such that the hydroxyl equivalent weight is up to 250, x is a number from 1 to 2, R 2 is hydrogen, alkyl having 1 to 6 carbon atoms, or phenyl, o is a number from 1 to 4 and p is 0 or 1. 3. The polyurethane polymer of claim 1 or 2, which contains no more than 10 ppm of zinc, tin and mercury combined and, except for the alkoxylated Mannich base, no more than 0.05 weight percent of amine group-containing