In a recent discussion with Carter I proposed a new
octahedron puzzle with revolving faces. Notice the
difference with Trajber's octahedron which is a puzzle
with revolving corners. This is what my proposal
would look like:



Notice that the "rainbow cube" is a truncated version
of this puzzle with only the centers and edges.

Moreover I have realized that the same triangular
face shape could be used to build an icosahedron !
Putting together 20 such triangular faces will result
in an icosahedron puzzle with revolving faces.

Anybody has ideas for internal mechanisms ?

Now the hard part: designing the insides! Good luck. I want to buy your first one.

Claude,

You said:
> Moreover I have realized that the same triangular face shape could be used to build
> an icosahedron ! Putting together 20 such triangular faces will result in an icosahedron
> puzzle with revolving faces.

I think you are mistaken. The lines over the surface will not lie in a single plane any more. The short lines seem to cut off pentagonal tips, and your cutting planes around the faces includes two of the short lines at each of the three corners it goes around.

Therefore you would either have to use a flexing mechanism (like impossiball), or cut the corners differently which leads to more pieces (but you need not include them all).

Jaap

Offhand I would consider using hte center piece of the face as the axis. Designing an 8 armed spider at that point would be a trivial job. Making the corner pieces stay together might be a bit trickier.

Hmm... I might have to prototype that thing after my order 4 pyraminx...

OK, so I find a simple argument to convince
myself that the icosahedron would need slightly
more complicated faces as suggested by Jaap:



I am not certain yet what exactly is the angle
of the purple little pieces, or if the angle is
small enough to ignore them and leave a small gap.

However the result would still look like
the following icosahedron but with the extra cuts.

I would love to have 1 to please. Use the 4 arm mechanism sort of like rubik's does except that is 6 not 4. I think it will be easyer. I'm guessing.

I'm not doubting that such a puzzle could be constructed, but I can't quite see how you could make one from the 14-sided rainbow puzzle. How would you transform the square side of the rainbow puzzle into the triangle-shaped faces of the icosohedron?

How about twisting "tips" the size of five whole triangular faces + from every other neigbouring face: one corner piece, and from the remaining neigbouring faces: two corner pieces, two connenting center pieces and one edge piece?
In the picture (found in another post) a line could be drawn, cutting five pieces each from the red and the light blue faces, and one piece each from the white and the yellow faces.

Is this at all possible? Some of the corners have to be moving, and I guess that might be a problem... Perhas a Skewb-like mechanism could be concived, with half the corners, or so, fixed in position, and the other moving.

Any thoughts?

Karl Wassholm

Claude only suggested that the octahedron is related to the Rainbow Cube. Certain pieces move exactly the same way, and the rainbow/dino cube mechanism is a good basis to start from when designing a face turning octahedron (though it would be very hard to make one from it).

The icosahedron is a completely different animal.

Jaap,

see below a picture of the corresponding
icosahedron puzzle:



it's made of paper and I had trouble
keeping it together to take pictures but
it gives a fairly good idea of what the
result would be. On the next picture I have
outlined in RED the lines that would be involved
in the rotation of the front purple face:



Don't you agree that they all lie in a
single plane since their distance to the
plane of the purple face appear to be equal ???

I am NOT 100% sure, please let me know what you think.

I once wondered how one could make a face turning icosahedron puzzle. Looking at those pictures though, it looks like it would be really hard to keep the corners on.