Recent studies show that copy number polymorphisms (CNPs), defined as genome segments that are polymorphic with regard to genomic copy number and segregate at greater than 1% frequency in the populations, are associated with various diseases. Since rare copy number variations (CNVs) and CNPs bear different characteristics, the problem of discovering CNPs presents opportunities beyond what is available to algorithms that are designed to identify rare CNVs. We present a method for identifying and genotyping common CNPs. The proposed method, POLYGON, produces copy number genotypes of the samples at each CNP and fine-tunes its boundaries by framing CNP identification and genotyping as an optimization problem with an explicitly formulated objective function. We apply POLYGON to data from hundreds of samples and demonstrate that it significantly improves the performance of existing single-sample CNV identification methods. We also demonstrate its superior performance as compared to two other CNP identification/genotyping methods.