Message #3862

From: zhulama@gmail.com
Subject: Solved 3^5, 3^6 and 3^7
Date: Thu, 07 Dec 2017 21:23:44 +0000

Hi, Everybody!

This is just an announcement that I’ve successfully solved all "cubes" from 4D to 7D so I’m sharing some tips and tricks so you can do it!

If you have solved the 4D cube, you can solve 5D, 6D and 7D with help of few simple tricks (no, the magicians don’t hate me because of those simple tricks!)

The trick to making easy 4D algorithms is to make a known 3D algorithm, then do a single "strategic" 4D move, then reverse the 3D algorithm and finally reverse the 4D move.

It’s also easy to make a two color 3-cycle macro, then you can make a three color 3-cycle macro by doing two color macro, strategic move(s) and reversing the two color macro.

4 color macro is made by doing a 3 color macro, strategic move(s) and reversing the 3 color macro… all the way up to 7 colors!

This is all extremely easy in MC7D software because you can create commutators by just pressing F1, known macro, F2, strategic move(s), F4! (this does macro, move(s), undo macro, undo move(s))

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To realize how the higher dimension cubes work, (in MC7D), it’s best to "turn off" of all pieces except for 1C and 2C pieces (simple check-boxes in MC7D).

When you do this for 5D cube, you can see two extra 2C pieces "inside the cube" (compared to 4D). They are on the left/right side of every center 1C piece. The extra dimension must be projected somewhere and this is a good place to do it.

6D cube adds extra two 2C pieces for every color, also next to the center 1C piece, let’s call them front/back

7D cube adds two more, let’s call them top/bottom.

Therefore, 7D cube has 3 main dimensions that we are constantly looking at, the fourth dimension is presented by extra cubes around the middle cube (just like 4D projection) and there are also 3 secondary dimensions shown "inside" the cube. I will talk just about 7D cube from now on.

Now when we understand 1C and 2C pieces, what about the rest?

When you turn on 3C pieces, they appear inside the cubes next to 2C pieces (it makes the "inside of the cube" fill up a little), some more appear next to 2C pieces on the sides and some new 3C pieces appear on the edge of every cube!

4C pieces appear next to 3C pieces on the inside, next to 3C pieces on sides and edges, and "new" 4C pieces appear in corners. The inside is completely filled up at this point

5C pieces appear next to 4C pieces on the outside (sides, edges and corners), this makes the sides completely filled up

6C pieces appear next to 5C pieces on the outside (edges and corners), this maxes the edges completely filled up

7C pieces are the last, they appear next to 6C pieces in corners and this fills up the cube completely.

This "filling up" from the inside to the outside makes the "fractal projection" of MC7D, it’s very good once you get used to it and it almost feels like cheating, that’s how good it is!

7D (and 6D) cubes has some interesting properties that 5D and lesser cubes don’t have!

There are some cubies that are "invisible" unless you look around the whole cube even in secondary dimensions. 6D only has a couple of invisible 2C pieces while 7D has a lot of invisible 2C pieces and some invisible 3C pieces.

When solving the cube, it’s the best to solve those first and then you can solve the rest of the cube without ever looking around secondary dimensions again!

…. will continue later when I find some more time.