Coxeter Plane projections

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Benoit
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Coxeter Plane projections

Post by Benoit » Thu Jan 03, 2019 6:14 pm

Good day everyone

obviously, someone has succeeded in using Stella to produce the projection on Coxeter planes of various 4D polytopes, including the omnitruncated 120-cell (333-Gidpixhi in Stella's database). See indeed this wikipedia page: https://commons.wikimedia.org/wiki/File ... 123_H3.png

After something like 45 minutes of searching for a way to do this in Stella, I give up and decided I should ask this forum.

Regards
Benoit
PS: I use the latest version of Stella4D v5.4

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robertw
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Re: Coxeter Plane projections

Post by robertw » Fri Jan 04, 2019 2:09 am

Hi Benoit,

So I think you just want an orthogonal projection rather than a perspective one. You can do this by selecting "View->Orthogonal View" (keyboard shortcut: o)

You may also want to select one of the cells and use "View->Orientation->Look at Selected Cell..." to align the model nicely.

And then hit Ctrl+Shift+H to hide all the cells, leaving just the edges and vertices (you'll want to make sure those are displayed first).

Benoit
Posts: 5
Joined: Thu Jan 03, 2019 6:05 pm
Location: Waterloo, Ontario, Canada

Re: Coxeter Plane projections

Post by Benoit » Sat Jan 05, 2019 9:02 pm

Thanks Robert.

This provide me lots of different projections, but I am not able to replicate the simple image for the 333-Gidpixhi I can find on Wikipedia, and neither am I able to get the other reflections. It is possible the author of that imagine has better knowledge of these Coxeter planes than I do and therefore knows which cell to select.

Benoit

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robertw
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Re: Coxeter Plane projections

Post by robertw » Sun Jan 06, 2019 3:11 am

It's just a cell-first projection based on the truncated icosidodecahedron cells (green by default). So select one of those, use "View->Orientation->Look at Selected Cell..." to look down that axis, hide all the cells with Ctrl+Shift+H to only show edges/vertices, and of course hit "o" if you didn't already to use orthogonal projection.

That looks the same for me as on wikipedia, but slightly rotated around the axis out of the screen. You could line this up manually using Left+Right-drag or Middle-drag with the mouse.

Pick a different type of cell at the start to get other projections.

Benoit
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Joined: Thu Jan 03, 2019 6:05 pm
Location: Waterloo, Ontario, Canada

Re: Coxeter Plane projections

Post by Benoit » Sun Jan 06, 2019 6:49 pm

Thank you Robert, I really appreciate your patience.

I hid all but the green cells, and I tried with quite a few of the green cells. I attach here two trials. None were successful in getting me anywhere near the wikipedia image. I must be doing something wrong.

ImageImage

ImageImage

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robertw
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Re: Coxeter Plane projections

Post by robertw » Mon Jan 07, 2019 1:48 am

Hmm, not sure what's wrong. It doesn't matter which green cell you select. The important thing is to use "View->Orientation->Look at Selected Cell..." after selecting the cell, and then don't rotate the view again.

After selecting cell:

Image

After "View->Orientation->Look at Selected Cell..."

Image

After hiding all the cells:

Image

Benoit
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Location: Waterloo, Ontario, Canada

Re: Coxeter Plane projections

Post by Benoit » Mon Jan 07, 2019 6:23 pm

Thank you for your patience. For some weird reason, quitting the program, restarting it, and then following these steps made it work.

Benoit

Benoit
Posts: 5
Joined: Thu Jan 03, 2019 6:05 pm
Location: Waterloo, Ontario, Canada

Re: Coxeter Plane projections

Post by Benoit » Mon Jan 07, 2019 6:53 pm

I was able to replicate the issue
  • From 4D menu, do an "edge first" rotation
  • Select a green cell
  • Look at selected cell
  • Hide the cell
the result is not the same at all, and actually not as "clean"
Image

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robertw
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Re: Coxeter Plane projections

Post by robertw » Tue Jan 08, 2019 2:41 am

Ah that makes sense. Looking at the cell just changes the 3D rotation, so if you change the way it projects from 4D to 3D, then this won't be altered. So yes, leave it at the default projection.

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