How about a Mixup Astrominx?

After seeing Oskar's Fudball puzzle, which is based on similar geometry, it seems like it wouldn't be too hard to make.

If I understand things correctly the Astrominx is a shape mode of the Starminx. The Fudball is a fudged slice-turn-only mixup starminx in the shape of a sphere. Its fudged such that the paths cross as 60 degrees so the slice layer parts are broken up into equilateral triangle. You could also try to fudge it such that the paths cross at 90 degrees but I suspect the degree of fudging required to do that would be very high.

Anyways... the whole point is the Fudball isn't a "similar" geometry... it IS the same geometry. So a Fudball in the shape of an isohedron could be called a Mixup Astrominx if you like. Personally I'd rather see it in the shape of a dodecahedron but both options would show the significance of the orientation of each piece.

Carl

It is the same puzzle, but because of the way the pieces are cut on the Astrominx (the Megaminx corners are exposed because of the shape of the puzzle), you end up with hexagonal pieces with small triangles in between, instead of rows of triangles...

The Megaminx corners ARE there on the Fudball see this picture:

If you cut this into the shape of an isohedron you could expose this corner... note it would be part of the core on a slice-turn-only puzzle. I still think the puzzle you are after is just a shape mod of the Fudball.

What I can't tell from this picture is if Oskar just fudged the sliding pieces into equilaterial triangles or if he also fudged the core such that the paths cross at exactly 60 degrees. I think both should be done for this puzzles to work at its best. I guess I need to go and work out at what angle the cut planes of a pentultimate cross. Maybe its already 60 degrees... but if so then I don't understand why the triangles are isosceles on the Soccer Slide. Hmmm...

Carl

Ok... If I've done the math correctly you'd need to fudge a 58.282525588538994675786096860227 degree angle into a 60 degree angle. A change that small I could see being undetectable in a picture like the above and you might even be able to get away without fudging it at all.

Hmmm...
Carl

Carl, I am not 100% sure what angle you are talking about but, what I have already written on a site of topic of Soccer Slide (answering to your post), the trajectories of belts in Soccer Slide intersect each other under an angle of 63:26:06 degrees (63,434948822922 deg = 1,10714871779409 rad)

Iwona

Yes, I saw that. And to be honest I'm not sure who is correct. I cheated when I got the above number and googled the angle between two faces of a dodecahedron. This should be the same angle between the slice layer planes of a Pentultimate as they are parallel to the faces. And your belts run along these planes. Here is the website I found:

http://members.tripod.com/paul_kirby/Linear/dodoca.html

And if I understand it correctly it says the answer is 2*cos-1 (.5/sin72). This is 116.565 and the supplementary angle of that is 180-116.565 or 63.435. Ok... forget everything I just said. I swear the last time I did this I got 58.2825 and I now don't have a clue what error I made. Boy... I've now burned 30 years worth of mistakes with my once every 10 years allowance.

And I though I was good at math,
Carl