Another miscellaneous thought on the dovetail topic. The way I
understand it is that each piece is dovetailed into the surrounding pieces.
I.E. on the 3x3x3 the face-centers are dovetailed into the edges which are
dovetailed into the corners. Now, the maximum radius of the dovetailing circle
permits this all the way out to 5x5x5, but at 6x6x6, a piece hangs outside the
dovetail radius.
The master design could work still. First of all, keep those cubes
nested together. Second of all, dovetail the inner cubes outward, so the whole
damn thing holds. Last, and certainly not least, in the case of the 6x6x6, I
think that we can add in another circle of dovetails at the radius which would
support a 7x7x7 cube.

This is really hard to explain without graphics, but try to imagine
this. Each dovetail ring will be a simple circle. Draw a 3x3 grid, and
superimpose a circle with a radius of 1.5 grids. Now, that will be
the inside of the dovetail, 1/3 of the way into the face. For a 5x5 grid,
repeat the 3x3 procedure and do the same for the 5x5, except at 2.5 grids
radius. That represents the next layer of the cube.

Keeping the original Rubik concept of faces-edges-corners nesting in
mind, we keep building out this way. It probably will be damn inconvenient to
build the 7x7x7 cube this way, but I am reasonably sure that it will hold
together and still retain all the necessary movements from the original cube.

In the case of the 5x5x5 cube, it will look like this:

abcba
bdedb
cefec
bdedb
abcba

a is held by 2 b's.
b is held by c and d.
c is held by e.
d is held by 2 e's.
e is held by f.

The only real weak spot is c, but it is surrounded by b's and an e.

The 7x7x7 cube will look like this:

abcdcba
befgfeb
cfhihfc
dgijijd
cfhihfc
befgfeb
abcdcba

a is held by 2 b's.
b is held by c and e.
c is held by d and f.
d is held by g.
e is held by 2 f's.
f is held by h and g.
g is held by i.
h is held by 2 i's.
i is held by j.
j is the center.

Again, the problem shows up in d, g, and i. I think that this is unavoidable,
but since the 3x3x3 cube holds together in much the same way, I think that it
should be about as a 5x5x5 cube is compared to the 3x3x3 cube. Not much
difference. The only problem that I have had with my 5x5x5 cube is the edge
cubies, and as I have noted, the middle and third edges should be the problems,
since everything else is buried within a face.

I haven't built a prototype yet, but once I get finished with this
semester of college (my last one), I intend to start working on this in between
job-hunting and paying off loans. If anyone is interested in this idea, I
would like to start correspondence on this topic.

I have some diagrams available, but they don't come over too well in
ASCII. If you would like a copy of my preliminaries, please E-Mail me at the
following addresses. Thank you for your consideration.

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