Hi All, Ed Pegg and I have finished processing all the 3-connected planar graphs (for simples) and 2-connected planar graphs (min degree 3) up to and including 29 edges for Mrs Perkin's Quilts and Perfect Squares. Many new Mrs Perkin's Quilts have been discovered, and there is much data yet to be worked through in Quilts. With the squared square results, there is less data and we have complete counts. As a result, we have obtained all simple squared squares in orders 21,22,23,24,25,26,27,28 and compound squares in orders 24,25,26,27,28. We can confirm the existing counts (orders 21-27) in simples squared squares are correct and complete. This confirms the work of Duijvestijn (spss orders 21,22,23,24,25,26) and Skinner (spss order 27) We prove the number of simple squared squares in order 28 is 3001 (and find 29 new simples). We can confirm Willcocks order 24 square is the lowest order compound and the only one of this order, We prove the 2 known order 25 compounds complete order 25 compounds We prove the number of compound squares in order 26 is 16, and find 1 new order 26 compound We prove the number of compound squares in order 27 is 46, and find 7 new order 27 compounds We prove the number of compound squares in order 28 is 142, and find 41 new order 28 compounds http://www.squaring.net/sq/ss/spss/spss.html http://www.squaring.net/sq/ss/cpss/cpss.html http://www.squaring.net/downloads/downloads.html I now intend to write a paper with Ed Pegg, substantiating the above claims, I intend to publish on the Archivx, not having published anything I assume that's all that's needed for publication these days I have already given some data to Neil Sloanes OEIS, but need to update the order 28 term in simples and compounds. We can also create the long overdue number sequence for Perfect Squares; 1,8,12,27,162,457,1198,3143 Couldnt be done before now, because we didnt have the compound sequence, we didnt have that because we couldnt confirm the 4 terms required to initiate the sequence. McKay/Brinkmann's plantri performed perfectly as a generator of the required graph classes. The efficiency of plantri in fast run time and its production of complete graph classes of non-isomorphic graphs allowed the required computations for exhaustive enumeration to be performed in a reasonable time frame. cheers, Stuart ps I may do order 29 as well, but that will depend very much on how many people and computers I can gain the assistance of. After this effort, I need a break and have no intention of starting a big run any time in the near future Some of the identifier labels for the squares may need changing, and no doubt other issues, I say there are only 44 isomers of 1015B , if you insist on canonical bouwkampcode, 4 have to be flipped about the diagonal, creating 4 duplicate bouwkampcodes, reducing the total from 48 to 44