My initial computer program found 1,111 total solutions for levels 1-6 (those flat shapes) and the levels 7-13 the total solutions were 3,333 which, mathematically made sense - 4,444. But my definitions of 'mirror image' and 'rotation' duplication were not held true by the puzzle community.

This was pointed out to me when Jacques Haubrich, co-author of 'Compendium of Checkerboard Puzzles', ran my puzzle through his computer - A RISC-OS running on an ARM processor. He did in minutes what took weeks on my old system.

Basically our computer programs agreed on the 1,111 flat solutions but the counts for the 3 dimensional shapes were not similar due to different formulas used in 3D. The definitions by the puzzle community were a good standard to go on and the above list is based on that standard.