Dear Brillianteers,

This is a poster I'm making for Uni Open day students. The aim is to inspire them mathematically in an easy-going way (so mostly non-technical). At the same time it's showing off a project done by a lecturer and me.

Please let me know

things you like,

things that could be improved,

any mistakes,

if the QR codes work - they should link to some of the videos found here.

Cheers,

Rob

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TopNewestRoberto, this is a rich, fascinating poster, going beyond the usual charts of regular polyhedra. But I can't even read it! Even if I expanded it, the font is still too small. And I can't seem to be able to copy the image onto another image software where I can blow it up and read the details. So, how can I help with this?

Edit: Well, I can use Google to expand, but it feels like looking at the chart through a tube.

Edit 2: Okay, one suggestion I have for you is that it'd be nice if you could somehow demonstrate how a "cross-section" of a hyper-polytope is worked out. For example, show a hypercube and a typical cross-section through it. I know it's not so easy how to represent that, but it certainly be helpful for people trying to understand how to generalize from 3D to 4D. – Michael Mendrin · 1 year ago

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As for your suggestion for hyper-polygons, I agree this is a nice idea! I do not (yet) have the tools to represent a hyper-polygon like the hypercube in all of it's 4D glory but I think making the effort to do so will be worth it! I shall have a look into doing this, this weekend. Any suggestions for ways to do this? I feel a Schlegel Diagram will not be best for this job but maybe something like this will be better.

Thanks for the feedback. – Roberto Nicolaides · 1 year ago

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Forget Schlegal Diagram, I agree. The other idea is better, but let me think on this too. – Michael Mendrin · 1 year ago

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– Roberto Nicolaides · 1 year ago

Yes sorry, "poor" was a poor choice in words on my part. I think I understood what you meant.Log in to reply

– Michael Mendrin · 1 year ago

Okay, I just had my hike and thought this over. In short, I think the most painless way to try to illustrate how to find the cross-section of an hyper-polytope is to first note that any linear projection of one preserves straight lines and planes. Hence, you can literally, from the POV, knife right through any such linear projection of a hyper-polytope, and the image on the plane is then a projection of the cross-section polytope. For example, one classic linear projection of a hypercube is a cube inside another cube, connected at the vertices. I can cut this in half, ending up with a cross-section that is a square inside another square, connected at the vertices. This, of course, is a projection of a cube, which is one of the cross-section polytopes of the hypercube.Log in to reply

– Roberto Nicolaides · 1 year ago

This is a lovely way of seeing it :) I'll have a look at juggling some things around to make room for this. Thanks, much appreciated!Log in to reply

Wow, there's a lot of information contained in there!

Could you help add some information to the Regular Polyhedra wiki?

It would be great if you want to organize a session to talk about polytopes with the Brilliant community. If so, send me an email and we can discuss the details. – Calvin Lin Staff · 1 year ago

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With the sessions - I've read lots of things about regular polytopes over the summer (and find them fascinating!) but have not studied them formally yet and would feel uncomfortable sharing knowledge that I have not proven to myself to be true. I'll be sure to drop an email to you if\when this changes! :)

I have some code (Python 2) that can make pictures of polyhedra in relatively easily too. It specialises in taking 3D cross-sections of 4D shapes and 2D cross-sections of 3D shapes. If you know anywhere this can be useful, let me know. – Roberto Nicolaides · 1 year ago

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