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 Post subject: Glue/Bridge/Tunnel Bandaging on a 3x3x3
PostPosted: Sun Oct 27, 2013 5:40 pm 
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Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Ok... Oskar's Tunnel Cube got me thinking.

We currently have this DIY kit which allows us to build any of the 3563 variations where neighboring Face Centers, Edges, and Corners are glued together.
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But what if we wanted to include the core in this picture as well as fixing non-adjacent cubies in place relative to each other? Oskar's Tunnel cube raised my hopes that such a kit might be possible and it might even be doable inside the normal volume of the 3x3x3, i.e. one might be able to avoid using bridges and the unintentional bandaging created by bridges interfering with each other.

I through this quick table together and convinced myself that there are really only 16 types of Glue/Bridge/Tunnel Bandaging on a normal 3x3x3 and many of these are very closely related.
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I believe I see ways to make all of them by themselves. However some of them don't seem to play well with others. A prime example would be is it possible to add Type (1) bandaging from the above table to Oskar's Tunnel Cube without resorting to the need to add external bridges? Same question for Type (4)? Can the Type (9) tunnel already present in Oskar's Tunnel Cube be replaced with Type (10)?

I was hoping all of these could be combined in a general way if the 3x3x3 had enough shells added to it as Oskar has added shells to his Tunnel Cube. I'm now not sure that is possible, or if it is I suspect that it requires the use of BOTH tunnels and bridges.

I'd LOVE to be proven wrong,
Carl

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 Post subject: Re: Glue/Bridge/Tunnel Bandaging on a 3x3x3
PostPosted: Mon Oct 28, 2013 1:25 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Hi Carl,
Forgive me that I won't speak about mechanisms.

In my program I used only six different types of bonds/bridges because they are all that is needed to emulate all the blocks you enumerated:
corner-edge-bond
edge-face-bond
face-core-bond
corner-corner-bridge (one edge between them)
edge-edge-bridge (one face between them)
face-face-bridge (the core between them)
E.g. I do not see the need to implement your type 3 if one could implement it like the fused cube with a lot of traditional bonds.

Not all types I enumerated have to be possible at the same time for an arbitrary number.
Example: You need at most one face-core-bond or (alternatively) one face-core-face-block because other configurations with face-core-bonds (like your type 2) can be emulated by the DIY kit pieces.
Not speaking about the Slice cube (your type 16) which can be emulated by:
- Three corner-corner-bridges
- Numerous edge-edge-bridges
- Three face-face-bridges
- Maybe other mixtures.

Andreas


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