Since several people have successfully made pyraminx crystals now, it's probably about time to describe how to make a pentultimate out of one of them.

Oddly, building the crystal is the hard part. The subtlety in making a pentultimate mostly has to do with what pieces you glue together, and I'll explain that now.

Since the pentultimate is a deep cut puzzle, it's necessary to keep the pieces in between sides from free-floating. Technically speaking, this can be done by taking the six pairs of exactly opposite face pieces on the underlying megaminx and gluing exactly one of them in place. However, most of the ways of doing that result in very indirect forcing of things to stay in place, the result being a very loose puzzle which can easily break. There's one way of doing it which is clearly the best, since it allows quite a few pieces of both the megaminx and crystal layers to be glued to each other, resulting in a much more solid puzzle.

Pick a corner of the underlying megaminx. Glue in place the three face pieces which are closest to it and glue them in place so they can't spin. Then take the three face pieces which share two edges with pieces we just glued in place, and glue them in place as well. Finally, glue all edges which are shared by two of the face pieces we've glued, and all corners which are shared by three of them.

For the crystal layer, take the triangular piece above the corner you first picked and glue it, the three wedges it shares an edge with, and the three triangles on the other sides of those wedges, in place. Glue them to the mexaminx layer pieces which are glued in place as well.

Now for the build-up to the pentultimate. It's basically just this. Green represents the inner crystal. Red represents the next outer layer of pieces, and blue is the ubrella-like extensions of those pieces which hold everything down. The little red parallelograms are glued directly to the crystal edge pieces under them, and that keeps the puzzle together and the centers from sliding.

Here is a picture of what a Pentultimate for all of you that doesn't know what one looks like. It sort of reminds me that it looks like a skewb.

http://www.chrisandkori.us/fw/main/defa ... DocID=1422

Wow check this out. My diagram on the left (from Oct 2004) and yours on the right. I think we are on to something!

Chris

I was just wondering what a Master Pentultimate would look like because there is a Master Skewb. Just a idea I had . If anyone can draw that would be awesome.

http://twistypuzzles.com/cgi-bin/puzzle.cgi?pid=1353

Well the version I can visualize would look like a Pentultimate and a Megaminx crossed (actually more like a Supernova than a Megaminx, because the Supernova is deeper cut). Each pentagonal face would have a 5-pointed star embedded on it, in addition to the rotated pentagons they already have. The vertex where the points of the star and inner pentagon touch along an edge would have seven pieces that meet, so this would probably only be practical in a computer simulation. But the end result would be that each plane has three cuts, allowing face turns or midplane turns.

Chris