Wetten, dass..? vom 5. November

I have an idea of how to build a 7x7 Rubik's Cube or any other NxN cube with odd N. The first version is a cube that needs to be taken apart to make a turn, the second version can be turned almost like a normal cube. I have to admit though that I have no experience in building things like this so it might not work at all. I'm quite sure the take-apart version would work, but it's of course the less interesting one.

Take-Apart Version

The key idea is to really use 7x7x7 = 343 small cubies, which are connected by pins. Between every two cubies, there's a pin from one of them going into a hole of the other:

pins inside the cube

Which direction should the pins go? I.e. which of the two cubies has the pin, which has the hole? For this, let's use the Manhattan distance from the central cubie inside the cube. This central cubie has distance 0, then its six neighbours have distance 1, the face centers have distance 3, and the corner cubies have the largest distance, namely 9.

I've found two ways that work:

  1. Pins always go outwards. That is, between two cubies the pin goes from the cubie with the smaller distance into the cubie with the larger distance. This is used in the picture above.

  2. Like a checkerboard, the even-distance cubies have pins on all sides, the odd-distance cubies have holes on all sides. Except the outer sides of the face-cubies of course, since we want the cube to have a flat surface.

A "turn" is made by taking the cube apart like in the above picture, turning one of the two parts and putting them together again.

The pins between face cubies (=outer layer cubies) need to have "snap-in" pins between them so that you need a little force to take them apart. This will ensure that the cube as a whole doesn't fall apart. The pins between inner cubies and between inner cubies and face cubies need not snap in, they should slide off easily. They're only there to hold the inner cubies so that they don't fall out when the cube is taken apart for a "turn". Btw, the inner cubies are needed because otherwise you couldn't use any force pushing on the faces of the cube, which you'll need when you want to take it apart for a "turn".

This simple version could also be used for any NxN cube if N is odd. I don't know how to use it for an even N. I talked about big cubes in general with Peter Sebesteny a while ago and he said it's always easy to turn an odd NxN cube into an even (N+1)x(N+1) cube by splitting the axis cubies (like he did to go from 3x3 to 4x4), but I'm not sure this would work with my idea.

Turning Version

The above construction is ok and I think I'd like to have one, but of course I'd much rather have a cube that turns normally. So I tried to modify the take-apart mechanism to allow normal turns. Just imagine you had a take-apart version and simply turned it. The pins would carve circles into the other cubies. However, you'd need fewer pins because since the inner cubies can't fall out anymore you don't need pins between them. And if you shift the pins a bit then their circles could leave/enter the cube between the outer cubies. The face centers could be connected with the cube center inside, similar to the 3x3 cube (see the blue parts).

tracks in the cube for the wings

The pins should probably better not be round but instead be "wings", filling out the space they'd carve in their neighbour cubie. Also, for this construction, the first of the two possible pin directions (explained in the take-apart version) needs to be used, i.e. all pins/wings go outwards.

Some of these wings draw circles outside the cube, so they'd be seen when you make a turn. This might be solved by using "rounded" cubes like the olympic cubes. This might also result in more stable cubes.

Stefan Pochmann
Last modified: March 20 2007, 21:28:10