Message #3570

From: Eduard Baumann <ed.baumann@bluewin.ch>
Subject: Re: [MC4D] Re: MagicTile few colors
Date: Sat, 19 Nov 2016 15:45:02 +0100

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 joining theire corner-piece.
I think your twists are "compacted" afterward so intermediate progress is not visible anymore.

I have solved once the 5x5x5 but I can’t any similarity with
{3,4} 4-Color Orbifold B F0:0:0.8 V0.8:0:0.

Kind regards
Ed

—– Original Message —–
From: qqwref@yahoo.com [4D_Cubing]
To: 4D_Cubing@yahoogroups.com
Sent: Saturday, November 19, 2016 2:49 AM
Subject: [MC4D] Re: MagicTile few colors

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. Sometimes 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 pieces by intuitively solving them into place, or I might reduce the puzzle into something simpler (which I did with the cube/octahedron Super Chops, where 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 centers, and middle centers. I’d solve the corners first, intuitively, since a move 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 tiny centers (again OK) and then the only pure 3-cycle algorithm, of tiny centers - 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 quick) and then solving each vertex along with the surrounding 8 pieces. There are only two distinct vertices here. You can think of each vertex’s group as a "center" (corner) plus four "edges" (edge2 pieces) and four "corners" (centers). So then it’s somewhat like 5x5x5 supercube centers. I built most of it intuitively, for instance making "blocks" of two solved "edges" with a solved "corner" in between. By about 32 moves it looks like I had everything solved except two "corners", although we can consider it a 3-cycle because we have some identically colored "corners". Then I solved that 3-cycle 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