Polyhedra Viewer: Visualize relationships between convex regular-faced polyhedra • Hacker News Board

Re: Polyhedra Viewer: Visualize relationships between convex regular-faced polyhedra

#11

Post by knolan » Sun, Oct 24, 2021, 6:22 PM UTC

aj7 wrote: post #3

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.

That isn’t a convex polyhedron, A retroreflective surface would actually be the interface between tessellated cubes.

Re: Polyhedra Viewer: Visualize relationships between convex regular-faced polyhedra

#12

Post by yesenadam » Sun, Oct 24, 2021, 10:38 PM UTC

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

...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 (30 comments)

Blog posts about its creation: Making the Polyhedra Viewer https://blog.tessera.li/polyhedra

Re: Polyhedra Viewer: Visualize relationships between convex regular-faced polyhedra

#13

Post by aj7 » Wed, Oct 27, 2021, 5:34 AM UTC

gilleain wrote: post #6

aj7 wrote: post #3

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.

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.

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.

Re: Polyhedra Viewer: Visualize relationships between convex regular-faced polyhedra

#14

Post by dabed » Thu, Oct 28, 2021, 2:19 AM UTC

unclesaamm wrote: post #10

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

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