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Polyhedra Viewer: Visualize relationships between convex regular-faced polyhedra

133 points by lioeters 5y ago

mkl 5y ago
This is great! I think it really needs an undo button in the operations mode.
- lifthrasiir 5y ago
  Also shapes can be made arbitrary smaller. For example, tetrahedron -> rectify -> rectify -> contract will result in a smaller tetrahedron.
- fjfaase 5y ago
  Looks like you can use the back button of the browser for this. And a redo can be done by using the forward button of the browser.
aj7 5y ago
Unless someone can show me how to generate a corner cube prism (one of the most technologically important prisms, and quite simple), this is coloring. I tried for a while.
- gilleain 5y ago
  Is that a regular faced polyhedra? From a google search it seems like this is a class of shape that combines flat faces and curved ones.
  - aj7 5y ago
    It’s a cube truncated to preserve three adjacent faces. Both the solid prism and hollow (just mirror surfaces) work as practical retroreflectors. You can’t build machine tools, semiconductor processing tools, or accurately tighten the bolts that hold on a 777’s wing without them. If you have an array of them on the moon, you can measure the distance to the moon, at one instant, to an accuracy of a millimeter.
- knolan 5y ago
  That isn’t a convex polyhedron, A retroreflective surface would actually be the interface between tessellated cubes.
ChrisMarshallNY 5y ago
Very nice! Thanks so much for sharing it.
uwagar 5y ago
lovely!
Waterluvian 5y ago
I love this website. Wow. I think it accumulates a bit too much browser history but not a big deal. As a complete novice to geometry and topology, I find the classification of all kinds of types of polygons to be equal parts maddening and beautiful. It’s wild to me that we can classify what we do to any kind of geometry to get these subsets.
unclesaamm 5y ago
I love this! Relatedly, here is a plug of an interactive unfolding of 4d polytopes into their 3d faces that I made recently: https://sam.zhang.fyi/html/unfolding/index.html https://sam.zhang.fyi/html/unfolding/index.html
- dabed 5y ago
  "Beautifully, all unfoldings of the 4-cube, 4-simplex, and 4-orthoplex are nets." why? is it a theorem or is it obvious?
yesenadam 5y ago
So awesome. Nice work! Aw I thought this was very familiar! - I loved Nat Alison's 10 minute !!Con 2019 talk, about its creation: !!Con 2019 - We Love Polyhedra! (And So Should You!) https://www.youtube.com/watch?v=XjvyELtrPF4 https://www.youtube.com/watch?v=XjvyELtrPF4 ...It's been on HN before a few times, the only time it got any interest was as a 2018 ShowHN https://news.ycombinator.com/item?id=17685232 https://news.ycombinator.com/item?id=17685232 (30 comments) Blog posts about its creation: Making the Polyhedra Viewer https://blog.tessera.li/polyhedra https://blog.tessera.li/polyhedra

133 points by lioeters 5y ago

mkl 5y ago

This is great! I think it really needs an undo button in the operations mode.

lifthrasiir 5y ago
Also shapes can be made arbitrary smaller. For example, tetrahedron -> rectify -> rectify -> contract will result in a smaller tetrahedron.
fjfaase 5y ago
Looks like you can use the back button of the browser for this. And a redo can be done by using the forward button of the browser.

aj7 5y ago

Unless someone can show me how to generate a corner cube prism (one of the most technologically important prisms, and quite simple), this is coloring. I tried for a while.

gilleain 5y ago
Is that a regular faced polyhedra? From a google search it seems like this is a class of shape that combines flat faces and curved ones.
- aj7 5y ago
  It’s a cube truncated to preserve three adjacent faces. Both the solid prism and hollow (just mirror surfaces) work as practical retroreflectors. You can’t build machine tools, semiconductor processing tools, or accurately tighten the bolts that hold on a 777’s wing without them. If you have an array of them on the moon, you can measure the distance to the moon, at one instant, to an accuracy of a millimeter.
knolan 5y ago
That isn’t a convex polyhedron, A retroreflective surface would actually be the interface between tessellated cubes.

ChrisMarshallNY 5y ago

Very nice! Thanks so much for sharing it.

uwagar 5y ago

lovely!

Waterluvian 5y ago

I love this website. Wow. I think it accumulates a bit too much browser history but not a big deal. As a complete novice to geometry and topology, I find the classification of all kinds of types of polygons to be equal parts maddening and beautiful. It’s wild to me that we can classify what we do to any kind of geometry to get these subsets.

unclesaamm 5y ago

I love this! Relatedly, here is a plug of an interactive unfolding of 4d polytopes into their 3d faces that I made recently: https://sam.zhang.fyi/html/unfolding/index.html https://sam.zhang.fyi/html/unfolding/index.html

dabed 5y ago
"Beautifully, all unfoldings of the 4-cube, 4-simplex, and 4-orthoplex are nets." why? is it a theorem or is it obvious?

yesenadam 5y ago

So awesome. Nice work! Aw I thought this was very familiar! - I loved Nat Alison's 10 minute !!Con 2019 talk, about its creation: !!Con 2019 - We Love Polyhedra! (And So Should You!) https://www.youtube.com/watch?v=XjvyELtrPF4 https://www.youtube.com/watch?v=XjvyELtrPF4 ...It's been on HN before a few times, the only time it got any interest was as a 2018 ShowHN https://news.ycombinator.com/item?id=17685232 https://news.ycombinator.com/item?id=17685232 (30 comments) Blog posts about its creation: Making the Polyhedra Viewer https://blog.tessera.li/polyhedra https://blog.tessera.li/polyhedra