Message #1449

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Social dream
Date: Tue, 22 Feb 2011 21:43:23 -0600

I like it :)

It would be good if we could come up with a way to specify the initial
orientation of the polytopes used to generate the axis set in a generic
manner, such that it didn’t have to be considered for each polytope. I’d
even prefer this if the chosen coordinate systems were not very natural for
some of the shapes. Like you say, difficult for human, but easy for the
program.

I also like Melinda’s suggestion to try to ensure everything is general if
possible. It feels like your thoughts extend perfectly well to 5D and other
dimensions. I’m not yet sure how to apply them to the hyperbolic puzzles of
MagicTile, but perhaps you already have thought about that and know how it
might go for MHT633?

Roice

On Tue, Feb 22, 2011 at 12:56 PM, Andrey <andreyastrelin@yahoo.com> wrote:

> Okay, let’s write fractions of full turn: 1/2,2/3,2/5,37/100 etc. It’s
> universal (in 4D puzzles) and not a big problem for programs.
>
> So twist record will look like 15:23:2/3:8 .
>
> To enumerate axes of the set we can select some coordinate system (that is
> natural for tesseract, 24-cell and duoprisms, and we can select something
> for 5-cell and 120-cell), get vectors of length 1 in directions of all axes,
> sort them in by w coordinate, then by z, by y and at last by x, and select
> the last (maximal) vector as 0, next as 1 and so on (for vectors greater
> than (0,0,0,0)). It may be difficult for human, but easy for the program.
>
> Andrey
>
> — In 4D_Cubing@yahoogroups.com, "Andrey" <andreyastrelin@…> wrote:
> >
> > I thought about usage of degrees (72, 120, 90,…) but it will not work
> for douprisms. Actually I want to have rational number there, but it’s more
> easy to write their common denominator is the head (near the set
> description) and show only numerators of the angle in all twists. We may
> write D=360 for all puzzles other than douprisms.
> > Or you want to write denominators only? Then again we’ll need two records
> for 144-deg rotation… Not good when we can select format with one record
> for every twist of the cell/face/edge/vertex…
> >
> > Andrey
> >
> > >
> > > But if I’m reading right, you are suggesting a 180-degree rotation on
> the
> > > 120-cell puzzle would be angle=30 (60/2). So the nature of the puzzle
> does
> > > seem to affect how the same twist angle is recorded. It feels like
> it’d be
> > > nicer if the recording of angles did not have this kind of dependency.
> > >
> > > seeya,
> > > Roice
> > >
> >
>
>
>
>
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