Point packings in the unit square are placements of n points in the unit square that maximize the minimum distance between any two of the points. Such packings are surrogates for the 2D-stock cutting problem. In this study we examine a unique representation for the point packing problem and extend the problem to higher dimensions and more complex shapes. The representation uses the Conway operator, a k-ary variation operator based on the lexicode algorithm. Three application of point packings are demonstrated. A parameter study for the Conway operator based algorithm is performed demonstrating that large populations are uniformly desirable but that the part of the operator that corresponds to mutation has a strongly problem dependent value for good performance. The three applications demonstrated are selecting well-space RGB color palettes, initialization of populations in an evolutionary optimizer, and fast clustering of codon usage data. Color palettes of different size are presented. The optimization application is found to gain substantial performance by using point packings as initializers. The bioinformatics application demonstrates significantly non-random clustering of a family of intrinsically disordered proteins known as dehydrins.