[next] [prev] [up] Date: Wed, 23 Sep 81 22:36:00 -0400 (EDT)
[next] [prev] [up] From: Dan Hoey <Hoey@CMU-10A >
~~~ ~~~ [up] Subject: Re: question for cube-lovers (S and T patterns)

It is impossible to put Z patterns on all six faces of the
cube, just as it is impossible to extend the Laughter (or Zig-Zag)
pattern to six faces. The problem is with the corners. If every
face is to have a pair of opposite corners that agree with the face
center and a pair of opposite corners that agree with each other
but not with the center, then the only constructible pattern is
like (i.e. M-conjugate to) the following:

F - U
- U -
U - F
D - L	F - R	U - R	B - L
- L -	- F -	- R -	- B -
L - D	R - F	R - U	L - B
B - D
- D -
D - B

But this pattern has incorrect corner orientation, and so is not

The T patterns were introduced to this list by David C.
Plummer [3 September 1980 2123-EDT], who assigns credit to Tanya
Sienko for the idea. Jim Saxe and I [27 January 1981 0102-EST] gave
a process for Tanya's T, the pattern that Minh Tai uses to sign
with. Our process, (FF UU)^3 (UU LR')^2, is four quarter-twists
shorter than Tai's ``quick routine'' because of the cancellation in
the middle. The other T pattern, Plummer's T, can be achieved in 28
qtw: FF UD' F'B' RR F'B U'D RL FF RL' UD' RL FF R'L U'D'.

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