The pyramorphinx looks deceptively simple.It's quite a chunky puzzle and a nice step up from the pyraminx.
The pyramorphinx is actually a 2x2x2 shape variant. If you can solve a pocket cube, you can solve this. The hard thing is to get used to which pieces are the equivalents of the 2x2x2 corners. The shape-changing also means that you have to concentrate hard to keep track of where you are in an algorithm. If you have the puzzle in its solved shape (even if the pieces aren't positioned correctly), you can see how to map the puzzle onto the 2x2x2. Each face consists of 2 of the tetrahedron tips and 2 flat pieces (the tetrahedron face centres). Bearing in mind that the flat pieces don't show orientation, you can probably work out the rest from there. Failing that, visit Jaap's Puzzle Page for some more help.
The pyramorphinx is a Meffert's puzzle although there are some knock-off puzzles out there. This one in the picture has stickers which I struggle to prevent from peeling off - I'm holding out for the next run of tiled versions of the puzzle.