Date: 3 January 1982 17:00-EST
From: Alan Bawden
Subject: The Pyramid
To: ELF at MIT-DMS
cc: CUBE-LOVERS at MIT-MC
I know of no books about the pyramid, but I can vouch for the fact
that the pyramid is much easier than the cube. I have essentially ONE
tool that is sufficient for all manipulations. It isn't even a very
long one. It is in fact such an obvious tool to try that many people
have discovered it independently. I'll tell you what it is after I
insert the following spoiler warning:
*** SPOILER WARNING !!! *** If you wish to solve the pyramid
yourself, stop reading now!
First off, notice that the points of the pyramid can be rotated
independently of all the other pieces. Thus we can safely ignore
those pieces and simply twist them into position as the last step. So
from here on in, when I say to twist about a particular point, I mean
to grasp the larger sub-pyramid that shares that point with the entire
pyramid and rotate it. This motion always leaves the face opposite
the designated point fixed.
This is not analogous to the way we think about the cube. When
dealing with the cube we rotate a face, leaving the rest of the cube
fixed. When dealing with the pyramid I am proposing to always rotate
everything BUT a face, a move that arranges to leave the four points
in the same position.
Having how described what I mean by a move, the actual tool is easy.
It's only four twists long. Chose any two points, call them A and B.
The tool is simply AB'A'B. It permutes three edge pieces that share
a common face, it flips two of those pieces over, and everything else
is untouched.
Since everything except the edge pieces can be placed in position
trivially (both the point pieces and the third kind of piece I haven't
mentioned yet), this tool might be sufficient (after arranging
everything else). I don't know if it is in fact sufficient since I
also employ some conjugates (like CAB'A'BC') in my solution.
I leave the details of actually applying this tool for you to
discover by yourself.
-Alan