Below are some images showing how some interesting new puzzles would look, if they could be built

The screenshots are taken from my Great Stella program, but I should point out that it won't allow you to actually twist the puzzles, only see where the slicing lines would go.

There was talk recently (started by Bram Cohen) about how a Pentultimate might be built. Well, if one does ever get built, here are some interesting modifications that could be made.

The Rhombicultimate: a rhombic triacontahedron with the Pentultimate mechanism inside. I think this would probably be the best embodiment for the puzzle, with correct orientation of both triangular and pentagonal parts required.


The Cubultimate: a cube with the Pentultimate mechanism inside. This is truly bizarre, and would be extremely disorienting! Any twisting and the puzzle will immediately lose its cube shape. As with the Pentultimate, 1/5th turns are required. The puzzle could be a single colour and still be quite hard. I think a lot of people would even have trouble mixing this one up!


The Octultimate: similar, but now in octahedron shape.


The Pyrultimate: similar again, but now in tetrahedron shape.


Even seeing these strange beasts its hard to imagine how they twist. I might make a cardboard model which twists along only a single plane, just to see how it looks.

Rob.

Would these puzzles turn in half if they were ever made. I am just trying to think of a type of mechanism. If they do turn in equal halves than maybe a skewb type spindle would work, maybe with a couple more arms :) ?
very awesome!!
Jake

The slices go through the centre of the model, if that's what you mean. I probably should have included a picture of the pentultimate itself for those who don't know what I'm talking about. There's a picture here:
http://www.chrisandkori.com/pentultimate.htm.

All the puzzles above would use the same mechanism inside.

It can not be made in a similar way to the skewb. They were lucky with the skewb! Although slices go right through the centre, it still turned out that four corners could be attached to a central spider mechanism. The pentultimate can't be constructed in this way. Any piece may move around the puzzle with respect to any other piece.

I think the cubultimate would be an awesome puzzle! I think people would be able to pick it up and figure out how to turn it initially. The slice lines continue visually around the puzzle so you can see where to turn it (unlike the skewb, where I've seen people spend five minutes just trying to make anything move!). However, they may take a while to realise at what points the twist can stop to allow a second twist. You have to turn 360 degrees to get back to a cube shape, and then you haven't messed it up at all. So the trick is to stop after only a 1/5th turn (72 degrees). The real look of horror would then come over their face when they manage a second twist, at a point which would just seem like mid-turn!

The Rhumbicultimate wins the the best shape category hands down. Your coloration may be a little mean though; With all those repeated colors it could take quite a bit of thinking just to figure out what piece is supposed to go where.

The square-1 suffers from much the same problem as the cubultimate - most people can't even figure out how to turn it.

That second twist would probably make most people outright drop the cubultimate. Breaking orthogonality is a serious taboo in western culture.

I'm intrigued by your coloring of the rhombicultimate - Are any of the pieces identical? If not, is there more than one coloration with that property?

> Breaking orthogonality is a serious taboo in
> western culture

Maybe it would be popular in Eastern countries then :-)

It's similar I guess to Fisher's Golden Cube, but probably more confusing!

My colouring for the Rhombicultimate uses five colours. There are six faces of each colour. Colours surround each 5-fold vertex in a different order. I think all the pieces are different. The six faces of any one colour lie in the face-planes of a cube. If you construct the cube for each of the five colours you get the familiar (to some) compound of five cubes (it is a "stellation" of the rhombic triacontahedron).

I think this colouring would work very well. There is no other five-colour colouring with these properties.