Hi, I'm back!

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Hi, I'm back!

Postby PWrong » Wed Jul 23, 2014 4:54 am

Hi everyone. I can't remember the last time I posted here but it was several years ago. For those who don't know me I used to post here a lot and I did a lot of the maths and notation for the toratopes. It's really great to see this is still going and people are still posting here.

I've recently submitted my PhD thesis in dynamical billiards, which you can read here.
Dimensional Characteristics of the Non-wandering Sets of Open Billiards
You'll be happy to know that some of my results apply in any dimension.

I was thinking now that I have some free time I should come back and relearn all this stuff. But as well as that, I was wondering if anyone would be interested in publishing some of the results we worked on this forum in a mathematics journal? There's some really original stuff here and I think more people should know about it. We could all be joint authors or something?

I can't guarantee I'll remember to come back here consistently since I have a lot of things on my plate at the moment. But I think I'll get emails whenever I get a reply to this thread. Also if anyone wants to add me on Facebook, send me a message.
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Re: Hi, I'm back!

Postby student91 » Wed Jul 23, 2014 12:51 pm

PWrong wrote:Hi everyone. I can't remember the last time I posted here but it was several years ago. For those who don't know me I used to post here a lot and I did a lot of the maths and notation for the toratopes. It's really great to see this is still going and people are still posting here.

I've recently submitted my PhD thesis in dynamical billiards, which you can read here.
Dimensional Characteristics of the Non-wandering Sets of Open Billiards
You'll be happy to know that some of my results apply in any dimension.
That sounds interesting. I guess I will read that when I have time. Great to have someone back on this forum who has been so important in the development of toratopes
I was thinking now that I have some free time I should come back and relearn all this stuff. But as well as that, I was wondering if anyone would be interested in publishing some of the results we worked on this forum in a mathematics journal? There's some really original stuff here and I think more people should know about it. We could all be joint authors or something?
In fact the CRF-project has been flourishing hugely, with much newly discovered polytopes in february 2014. We tend to call that february CRFebruary. It gave a huge amound of posts in the "Johnsonian polytopes" topic (it hit 50+ pages), which made Keji decide to split this to a separate forum.
Following these discoveries we discovered an underlying process to make structures of these polytopes from uniforms (and regulars) in the icosahedral/600-cell group. Quickfur was the first to discover this. He made a nice animation of ike expanding into a bilbiro:
Image
and ike expanding into a thawro:
Image These discoveries where so new and the underlying process of partial stott-expansion was so interesting, that we decided to publish an article about it. The topic Construction of BT-polytopes via partial Stott-expansion is practically dedicated to that. Most new polytopes can be found here, though the newest discoveries, those that are true partial expansions of ex, are mostly not included in this index, because quickfur hasn't been active for a few weeks now, and thus we lack pictures to make the wiki pages interesting.
On the toratope area there is a guy called ICD5N, who has been able to make nice gifs of toratope sections and rotations. He apparently has posted these on reddit. Just yesterday a new guy called Nate has thought of using sound as a medium to explore toratopes. As I am mainly busy with the polytopes, I had no Idea on what to answer to him, so I thought maybe someone else knows enough of toratopes to help him exploring these shapes.


sincerely student91.
How easily one gives his confidence to persons who know how to give themselves the appearance of more knowledge, when this knowledge has been drawn from a foreign source.
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Re: Hi, I'm back!

Postby ICN5D » Wed Jul 23, 2014 5:07 pm

Well, hey there, PWrong! I've read many a post from you, dated back then. It's great to see you come back. I was wondering when that would happen! So, in the last nine months, I've learned a ridiculous amount regarding toratope notation, implicit functions, rendering, construction, etc. It was mostly due to Marek and I going back and forth, thanks to his thirst for answering questions, and my asking of them. You'll see a lot of awesome graphics of toratopes on " The Tiger Explained" thread. That's my latest addition. And, in the last few days, I've been posting them on Reddit, /r/mathpics , /r/educationalgifs , and some others have cross posted for me. It's just not right that the HDDB is as quiet as it is. So, I decided to reach out to some other math communities. And, it looks like 3 new people have registered from that. Very cool. Glad to have another toratopist back on here. This stuff should be published, absolutely. I have zero academic background, but a lot of time to be proficient in learning it.
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Re: Hi, I'm back!

Postby PWrong » Fri Jul 25, 2014 3:53 am

It's great to meet you, I'm really glad to see you've made all this progress.

In fact the CRF-project has been flourishing hugely, with much newly discovered polytopes in february 2014. We tend to call that february CRFebruary. It gave a huge amound of posts in the "Johnsonian polytopes" topic (it hit 50+ pages), which made Keji decide to split this to a separate forum.


That sounds cool but I completely missed that and I have no idea what's going on there. Which thread should I read first to get an introduction to this idea?

This stuff should be published, absolutely. I have zero academic background, but a lot of time to be proficient in learning it.

OK well I've published two articles from my PhD work and I have two more on the way. So I could do all the writing and LaTeX work (at least for the toratope material), and check everything with my supervisor to see what he thinks. It'll be good for me to get my publication count up. We'll need to decide exactly what we want to publish and in how many articles, and pick a consistent notation (preferably as similar to conventional mathematics notation as is reasonable, or at least with a very clear translation from our notation into conventional notation). I'll start a new thread on this. Maybe it might even need a new forum.
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Re: Hi, I'm back!

Postby wendy » Fri Jul 25, 2014 4:48 am

Welcome back.

CRF is the latest project to fid 4d johnsons,
The dream you dream alone is only a dream
the dream we dream together is reality.
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Re: Hi, I'm back!

Postby student91 » Fri Jul 25, 2014 10:47 am

PWrong wrote:
[...]

That sounds cool but I completely missed that and I have no idea what's going on there. Which thread should I read first to get an introduction to this idea?
The (15-pages long :\ ) topic "bilbirothawroids" is the split that includes almost all discoveries of CRFebruary. Back then I tried to find these by contracting ids to bilbiros and thawroes, and quickfur was very good at finding them in a seemingly less structured way which gave more interesting polytopes. If you have loads of free time you can read all this, but the most important things are the first post, which started it all, the discovery of the J92 rhombochoron (incmat here), the invention of the CVP-tool (a tool that gives a measure of the intrinsic complexity of polytopes, it might come in handy some time. The last/recent definition can be found here), and the discovery of node-changing, which can be found here, and a summary here. The other posts of the Bilbirothawroid topic are mostly about individual discoveries, naming schemes and (sometimes very unwieldy) speculations about underlying structures.
The now used process to construct these shapes is by partial expansion. The same partial expansion Klitzing has a page about on his site, but now with a step in which you change some nodes from x in (-x), with the necessary value-adding. This node-changing if interpreted as things you do to a shape are now mostly seen as taking a faceting of the polytope. The split about this discovey is "Partial Stott-expansion of nonconvex figures. student5 was the first to use the process as we use it now. After reading this post, and understanding the node-changing, I guess you will understand what we are doing to make these shapes. In the "Constructing BT-polytopes via partial Stott-expansion"-topic, we have used this to make some very interesting polytopes. I guess Klitzings elaborate expansion-posts will make the process even clearer. Basically you can do such an expansion on every reflective subsymmetry of a polytope, which is why a big part of this topic is about symmetry groups. Another part is about different definitions of "partial" (real boring, but necessary). Interesting things are from page 4. Introduction at page 1.
Also interesting is D4.11, see the topic "D4.10 and D4.11". It is the first thing which uses a 4-dimensional subsymmetry of ex.
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Re: Hi, I'm back!

Postby anderscolingustafson » Sun Jul 27, 2014 2:49 am

Welcome back PWrong :D
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