A table was created that shows how many unique lexicographically minimal tiles of each geometric configuration with n arms.
You can access the table here.
A description of the uses for this table can be found in the paper by T. Dickerson, J. Girard, B. Goodhue, D. Koch, A. Parent, and M. Spuches.
Thomas Dickerson's Octet Truss Tile Finder program can be downloaded from the "Available Software" section of the "Our Publications" page.