From @bullet.ecf.toronto.edu:tee@ecf.toronto.edu  Tue Dec 10 18:03:38 1991
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From: TEE  LUNS <tee@ecf.toronto.edu>
To: Cube-Lovers@ai.mit.edu
Subject: 7x7x7
Message-Id: <91Dec10.180328est.8345@bullet.ecf.toronto.edu>
Date: 	Tue, 10 Dec 1991 18:03:14 -0500

 
   I was reading through the archives the other night (just signed onto the
mailing list) and one of the last posts in cube-mail-7 triggered something in
me head.
 
   The suggestion was to use a fresnel saw to cut all the cubelets out of
a single chunk of material, with the cut such that the pieces all interlock.
The interlocking however doesn't need to be quite as intricate as the diagram
given - why not a simple dovetail?
 
    That's actually to some extent what the 3x3x3 cube is - the center cubelets
dovetail into the edge cubelets, and the edges dovetail into the corners. It
just happens that there's enough reduncancy that the outside half of the
dovetail joints can be disposed of, and the edges made straight while still
allowing the cube to stay in one piece.
 
    If we have a complete (both sides) locked dovetail, we can actually assemble
almost all of the cube out of the cubelets. Since the cubelets will always
require an entry point for their dovetail grooves, there will be a few cubelets
that have to be attached differently.

    The simplest solution I can think of is to have the dovetail/cublet pair
seperate, with a countersink on the dovetail, and holes through the other
cubelets so that we can screw the dovetails (which are already in their grooves)
onto the last couple of cubelets.

    One drawback with this approach is that the boundaries between layers of
cubelets will be quite jagged. If the dovetails go right to the surface, one
has to be *VERY* careful when turning the cube to make sure that all layers
are lined up in the axes that aren't being turned (this problem plagues the
magic truncated octahedron I have - pieces pop out all the time). The solution
is to make the dovetail taper off at its ends so that if it's out of line with
the groove its going into, it can still correct itself. This will lead to holes
at the surface though, so the cube won't be too pretty.

    A novelty with this approach though is that no centre is required. We
could build a hollow 3x3x3 cube with face centres hollow, and see right
through the cube. This should be possible with larger odd-sized cubes too,
but there comes a point (probably 7x7x7 again) where mechanical play would
let middle layers shear enough to pop out cubelets.

    But, if we had the smaller odd-sized cubes trapped inside, not only
would they help hold the outer layers together, if we made the cubelets 
mostly transparent, we'd be able to see  what we've had to imagine in the
past. Now that'd be one heck of a puzzle.