At the BCME 6 conference in Britain last month I caught up with John Hibbs (retired - but still very active - HMI) who discovered one of the original Size 3 Sphinx solutions. He had rediscovered the drawing of his solution, so, as an item of history a scan of it has been added to the record of his solution at:The fascination of the Sphinx seems to be in the way it replicates itself - 4 Sphinxes make a Sphinx is the starting point. Are there other shapes which behave this way? Certainly.
John has donated some work from an old notebook which might start you off on the hunt. Since this work can be seen as a What happens if...? question developing from the Sphinx problem, it has been recorded on Page 4 of the Sphinx Album.