I'm going to try my best to explain these, and also, pardon my crude MS paint sketches. Also, I'm not as skilled in AutoDesk Inventor as I am with AutoCAD, and I can't get a legal copy for free of AutoCAD, so my free student edition of Inventor is the best I can do.
1) I was looking through old topics today, the Helicopter Cube thread. I was reading the old posts and saw one my Bram mentioning the Square Anti-Prism. I then thought of the 2x2 made by P|astic, and it got me thinking... What about a Triangular Anti-Prism. After a couple more minutes of thinking, I realized that it is actually an octahedron. I was particularly looking at the 6 points when laying the top and bottom face together (sorry if that doesn't make sense). So my mind wandered to the Rubik's UFO. So the first image (if I get this right) should be an octahedron with red lines tracing how a Rubik's UFO would be planted.
2 & 3) A few weeks ago I was thinking of my favorite shape mod, the Hexagonal Dipyramid. So far it's only been applied to a 2x2, 3x3 and 4x4. Why not other puzzles. The next image should be some very crude sketches of a Skewb and Square-1 with lines marking the shape of a Hexagonal Dipyramid.
4 & 4.5) I made a thread in November 2006 (This thread for reference
) discussing some ideas for cylindrical 3x3 shape modifications. This is me elaborating on the diagonally placed mechanism inside a cylinder.
The first 3 images are from just making a 57mm diameter cylinder around a standard 57mm 3x3x3. The first two images are just two separate angles, while the other one was crudely drawn on in MS paint to show which pieces are what.
The next two images are when I truncate down the 2 opposite corners untouched from when the puzzle was shaped into a cylinder. I realized I truncated too far, as the triangle in the center of each circular face is actually the core.
The last 3 images are were I truncated down the corners a little bit less. I meant for the puzzle to be completely cylindrical, but I don't have enough skill nor patience to go in there and build up on the little grooves. I suppose it's a good thing, because those dips help identify the centers. The first two of the final three images are showing different angles while the final image on this post is using MS Paint to distinguish the different kinds of pieces like before.