A 10-to-1 compressed video of Noel's Magic120Cell solution. Happy Holidays!

## Saturday, December 20, 2008

## Sunday, December 14, 2008

### Magic120Cell Solved!

In a bit of a coincidence to the last post, the formidable permutation puzzle version of the 120 cell I published this year has been solved for the first time. Noel Chalmers posted this announcement to the 4D cubing group last night. I have genuinely wondered if this might never happen, and as a result feel a strange urge to alert the press!

I am relieved the software held up to the task. His solution had over 33 thousand moves, which took about 40 minutes just to play back on my computer using the fastest move speed. It feels really good to have had a hypercubing enthusiast put that much effort into something I helped create. A lot of love went into it earlier this year, and even as far back as 2006 when the hope of it was initially started, so it really is neat that an actual solution is now realized.

## Sunday, December 7, 2008

### 120 Cell Animations

Here are a couple quick videos of the 120 cell made for your enjoyment using 120 Cell Explorer. The animations show how the appearance of this object would change as we rotate our viewpoint around it in 4D.

Both show half of the 120 cells and color the cells based on which "ring" they are on. The highly symmetric 120 cell can be thought of as composed of 12 rings of 10 cells each, hence these animations are showing 6 of the 12 rings. One ring (the purple one) is more difficult to see because it is surrounded by the 5 others. All of the rings are linked to every other ring exactly once, so unless you were a magician, you couldn't pull any 2 of the rings apart without breaking one of them. Can you see the linking?

The next video is slightly more interesting to me. It is essentially identical to the first one except that we are starting from a different vantage point in 4D.

Both show half of the 120 cells and color the cells based on which "ring" they are on. The highly symmetric 120 cell can be thought of as composed of 12 rings of 10 cells each, hence these animations are showing 6 of the 12 rings. One ring (the purple one) is more difficult to see because it is surrounded by the 5 others. All of the rings are linked to every other ring exactly once, so unless you were a magician, you couldn't pull any 2 of the rings apart without breaking one of them. Can you see the linking?

The next video is slightly more interesting to me. It is essentially identical to the first one except that we are starting from a different vantage point in 4D.

## Wednesday, December 3, 2008

### G3D Blog

I started a Gravitation3D blog this week. Nope, I'm not masochistic and trying to burden myself with another project. On the contrary, I did it after getting a flux of questions about the same time I read this article from a coding blog I like. It took an hour or two to setup the new blog to a reasonable liking, but now every time I get a G3D question, I can answer it there instead of with an email (which would only shortly after be sentenced to a life term of solitude in my gmail). I don't get a lot of emails about G3D, but over time this will probably make it even less so. I figure this will bring me much closer to my lifelong goal of having no external sensory inputs impinge on my overly introverted self.

Why a wordpress blog this time instead of blogger? I've discovered wordpress has support for LaTex, which allows nice display of mathematical formulas, and I think this will be important for some G3D posts. There are roundabout ways to do this in blogger too (see here, here, or here), but I found this too troublesome - it didn't seem to work as well or look as nice as the native wordpress support.

Why a wordpress blog this time instead of blogger? I've discovered wordpress has support for LaTex, which allows nice display of mathematical formulas, and I think this will be important for some G3D posts. There are roundabout ways to do this in blogger too (see here, here, or here), but I found this too troublesome - it didn't seem to work as well or look as nice as the native wordpress support.

It's funny, since google gives you so much for free and at such high quality, I have found myself frustrated on more than one occasion when they haven't solved a problem for me that feels like it should be solved (like LaTex support for any html I publish). Once I'm aware of this reaction, I realize it's a ridiculous sentiment, but I'd be lying if I said it doesn't crop up now and then (No good deeds go unpunished).

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