Message #492

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] Magic120Cell Realized
Date: Sun, 04 May 2008 23:38:45 -0500

Honestly, the reason I wasn’t planning on working through a solution was
that I am a bit scared of the sheer number of pieces! I just finished up
the final parts that I felt were needed for it to be solvable today, and I
actually haven’t even figured out a single sequence yet. So as of this
evening, I only have the thoughts about it we’ve discussed in the past,
which is that it will be easier in some ways than MC4D because of the larger
space to sequester pieces, but that it will be a big effort in time. Also,
I think I am ready for a bit of a rest and was too excited to share to let
it sit on a shelf. Sarah will be happy to get my attention back now too
since I’ve been spending a lot of time on it lately :)

Since I haven’t been through it, I hope there are enough features for a
solution (there are no macros yet, and I could see that being the first
request as people start attacking it, but it will be a while before I look
at that). I think my fear at this point is that some stupid bug would
somehow corrupt someones solution after they worked on it for a long time!
Working through MC5D myself was able to quell that worry last time. But the
scrambling and autosolve has had a decent amount of exercise as I’ve worked
on it, so I think all should be ok.

Writing a general 4D puzzle engine certainly would be a huge achievement.
It was nice to be able to hardcode 120 cell characteristics throughout the
code, and I certainly did - I can’t imagine having worked without that
luxury at this point. I also realized through this effort that I understood
general 4D rotations very badly, and still do though I’ve improved a
little. It was so much easier when everything was coordinate axis aligned.
I was able to glean just enough from the results of a paper (
http://www.geometrictools.com/Documentation/RotationsFromPowerSeries.pdf),
which combined with some experimentation to figure out how to calculate the
rotation matrix coefficients allowed me to get working code for "simple
rotations". Wiki has some more info on that term if anyone is interested (
http://en.wikipedia.org/wiki/SO%284%29).

Anyway, I won’t go on too much for now, but I look forward to more
discussion about this puzzle. Thank you so much for your highly positive
email :)

Roice

On Sun, May 4, 2008 at 9:44 PM, Melinda Green <melinda@superliminal.com>
wrote:

> Roice rocks!!!
>
> Don and I have been cooking up plans to support more puzzles including
> this one in MC4D for some time but Roice beat us to the best one. The
> 120 cell holds a special place in the pantheon of regular polyhedra in
> all dimensions. It has no analog in any dimension greater than 4. If
> puzzles were planets, the 120 cell would be Saturn. Being the first to
> tame this beauty will earn you a special place in history, though the
> task may be as hard as being the first to visit Saturn. We’re lucky that
> Roice didn’t solve it before publishing it. Please tell us why, Roice?
> Did you try to but underestimate the difficulty or did you just want to
> give everyone a chance? The screen shots are amazingly beautiful and it
> is such a gift to the world that you would have been completely
> justified to have kept it secret until first solve.
>
> Thank you so much!
> -Melinda
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