Message #1412

From: Matthew <damienturtle@hotmail.co.uk>
Subject: Re: The 3 slice pentachoron
Date: Tue, 15 Feb 2011 18:24:33 -0000

With a little thought, the {3,3,3}3 puzzle (this can serve to check I’m thinking of the correct puzzle) is fairly easy to solve. The octahedra located around a vertex are one piece and can easily be orientated correctly, and the tetrahedra at each vertex are equivalent to the trivial tips on a pyraminx and thus are easy to solve in a similar manner, although you know all this already. This leaves the 10 edges which can be 3-cycled using basically the same 4-move sequence which applies on a normal pyraminx. This allows the sequence which flips 2 edges on a pyraminx to also apply. A slight change in 4D is similar to one found on the 3x3x3x3: you can have a single edge with incorrect orientation. Think about the previous sequence to flip 2 edges in place (switching 2 stickers on each, to clarify). Perform this, then perform a single twist about an edge to change the stickers being swapped on one of those edges. Then repeat (or undo) the flipping sequence and undo the edge twist. I will upload a log file demonstrating this after posting. Any more questions, just ask (I sometimes don’t explain things well).

Matt

PS. Funny coincidence, my Meffert’s Professor Pyraminx arrived today, so I might do the {3,3,3}5 for fun sometime soon. When/if I do, I can write a short guide if there is enough interest, although I feel that most of the fun in this group is covering new ground and solving puzzles with no tutorial to follow.

— In 4D_Cubing@yahoogroups.com, "Eduard" <baumann@…> wrote:
>
>
> I asked in this forum for instructions for the pentachoron (3 slices).
>
> Since I got no reaction I think that these instructions do not exist. At
> least not for a layered solution (as Roice’s for the magic cube). This
> is not astonishing because the pentachoron beeing smaller (only 5 cells
> compared with the 8 cells of the magic cube) seems to be more ensnared.
> Reading (watching, playing) the log files from R.Durka I can’t learn
> anything. Does he use computer aid?
>
> We can distinguish the following technics (1) fully by hand, (2) by hand
> and macros, (3) with heavy computer aid. I’m doing (2).
>
> Without any macros and commutators you can do the 5 faces with 4
> differently colored octahedra. Then the 5 fourcolored corners can be
> done with slice 3 twists only.
> After that you have the hard core of the job to be done: the 10
> threecolored edges. For the moment I have established a 3-cycles across
> an edge, a 3-cycle in a face and a 3-cycle around a vertex. I have also
> a concept for a sequence which mirrors two edges in their place. I need
> also a sequence to turn two edges in their place. All these sequences
> work with slice 2 twists of course.
>