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Thanks very much for carefully communicating your thougths.
I never preassemble super-pieces. Perhaps I should learn it.
Concerning
{3,4} 4-Color Orbifold B F0:0:0.8 V0.8:0:0
I can't follow your instructions.
Even replaying carefully your 52-Twist solution. I can only see the effect =
of the first two twists: edges at home.
But afterward: no progress can be observed with for the tiny edge2 pieces j=
oining theire corner-piece.
I think your twists are "compacted" afterward so intermediate progress is n=
ot visible anymore.
I have solved once the 5x5x5 but I can't any similarity with=20
{3,4} 4-Color Orbifold B F0:0:0.8 V0.8:0:0.
Kind regards
Ed
----- Original Message -----=20
From: qqwref@yahoo.com [4D_Cubing]=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Saturday, November 19, 2016 2:49 AM
Subject: [MC4D] Re: MagicTile few colors
=20=20=20=20
I also find 3-cycles on complex puzzles, although I am generally not very=
strict about what I try to find. The cycles do not need to be pure. I also=
don't try to find ways to orient puzzles, since I can usually either solve=
those with appropriate setup moves or by just doing two 3-cycles. Sometime=
s I find some unusual parity or orientation issues which I will figure out =
when they come up. Also, depending on the puzzle, I might solve a lot of pi=
eces by intuitively solving them into place, or I might reduce the puzzle i=
nto something simpler (which I did with the cube/octahedron Super Chops, wh=
ere my big first step was to build groups of pieces so I didn't need to use=
the edge twists anymore).
Here's an example of the nonpure cycle thing. Let's look at Dodecahedron =
E0:1:0.11, where we have corners, corner centers, edge centers, tiny center=
s, and middle centers. I'd solve the corners first, intuitively, since a mo=
ve is a 2-cycle. Then you can make an 8-move 3-cycle of corner centers that=
affects everything except corners and middle centers, but only corners are=
solved now, so it's OK. Then there's a 4-move 3-cycle of edge centers that=
also affects tiny centers and middle centers, but we haven't solved those =
yet so that's OK too. Now I have a 3-cycle of middle centers that affects t=
iny centers (again OK) and then the only pure 3-cycle algorithm, of tiny ce=
nters - that one is 14 moves.
For the puzzle you mentioned, {3,4} 4-Color Orbifold B F0:0:0.8 V0.8:0:0 =
on the program, I do puzzles of that type by doing the middle edges (very q=
uick) and then solving each vertex along with the surrounding 8 pieces. The=
re are only two distinct vertices here. You can think of each vertex's grou=
p as a "center" (corner) plus four "edges" (edge2 pieces) and four "corners=
" (centers). So then it's somewhat like 5x5x5 supercube centers. I built mo=
st of it intuitively, for instance making "blocks" of two solved "edges" wi=
th a solved "corner" in between. By about 32 moves it looks like I had ever=
ything solved except two "corners", although we can consider it a 3-cycle b=
ecause we have some identically colored "corners". Then I solved that 3-cyc=
le with an algorithm that roughly corresponds to the 3x3x3 algorithm: [R2 U=
' R2 U' R2 U2 R2, D']. Align the vertices and it's done.
--Michael
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