4 ms·

Polyhedra Viewer: app to explore the relationships and transformations between various convex polyhedra. This has been a passion project of mine for the last s

Polyhedra Viewer: app to explore the relationships and transformations between various convex polyhedra. This has been a passion project of mine for the last six months (with different versions going back further!) It's partially inspired by George W Hart's virtual polyhedra (http://www.georgehart.com/virtual-polyhedra/vp.html http://www.georgehart.com/virtual-polyhedra/vp.html) I wanted to make something accessible and beautiful, since a lot of the resources that already exist aren't very friendly to people not already obsessed with polyhedra. I'm still (sort of) working on it, so suggestions and comments are welcome!

kelsolaar 8y ago
Congratulations, lot of work put in a very well refined and presented page!
- tesseralis 8y ago
  Thank you! Did you make sure to check out the individual polyhedra (e.g. https://polyhedra.tessera.li/tetrahedron https://polyhedra.tessera.li/tetrahedron)
MrEldritch 8y ago
I immediately tried to construct my favorite obscure polyhedron (the rhombic dodecahedron) and found I simply could not take the dual of the cuboctahedron! :P That aside, this is a really fantastic little toy here - I'd never really understood the relationships between all these shapes before, or exactly what some of these operations were, geometrically speaking.
- tesseralis 8y ago
  Unfortunately the Catalan solids aren't in there yet, because I wanted to focus on the regular-faced polyhedra for now! Perhaps in a future update :)
- jacobolus 8y ago
  > favorite obscure polyhedron (the rhombic dodecahedron) Obscure? Come on! The rhombic dodecahedron is the Voronoi cell of the FCC lattice, making it (arguably) the most natural 3-dimensional analog of the hexagon. It shows up all over the place! You might enjoy these rhombic dodecahedral dice https://www.mathartfun.com/thedicelab.com/SpaceFillingDice.html https://www.mathartfun.com/thedicelab.com/SpaceFillingDice.h...
  - DonHopkins 8y ago
    I'd enjoy reading some more character analysis of obscure polyhedra. The Dodecahedron was the most multifaceted character in The Phantom Tollbooth! https://www.shmoop.com/phantom-tollbooth/dodecahedron.html https://www.shmoop.com/phantom-tollbooth/dodecahedron.html http://teacherwifey.blogspot.com/2014/08/the-phantom-tollbooth-dodecahedron.html http://teacherwifey.blogspot.com/2014/08/the-phantom-tollboo...
  - MrEldritch 8y ago
    It's "obscure" to me (and also my favorite) because I had never even heard of it before I tried to find out what the most natural 3-dimensional analog of the hexagon was. :)
    - jacobolus 8y ago
      Also see https://en.wikipedia.org/wiki/Kepler_conjecture https://en.wikipedia.org/wiki/Kepler_conjecture
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grey-area 8y ago
Is there any way to keep the objects spinning? It'd be nice if you gave them a flick and then they kept spinning under their own inertia.

kelsolaar 8y ago

Congratulations, lot of work put in a very well refined and presented page!

tesseralis 8y ago
Thank you! Did you make sure to check out the individual polyhedra (e.g. https://polyhedra.tessera.li/tetrahedron https://polyhedra.tessera.li/tetrahedron)

MrEldritch 8y ago

I immediately tried to construct my favorite obscure polyhedron (the rhombic dodecahedron) and found I simply could not take the dual of the cuboctahedron! :P That aside, this is a really fantastic little toy here - I'd never really understood the relationships between all these shapes before, or exactly what some of these operations were, geometrically speaking.

tesseralis 8y ago
Unfortunately the Catalan solids aren't in there yet, because I wanted to focus on the regular-faced polyhedra for now! Perhaps in a future update :)
jacobolus 8y ago
> favorite obscure polyhedron (the rhombic dodecahedron) Obscure? Come on! The rhombic dodecahedron is the Voronoi cell of the FCC lattice, making it (arguably) the most natural 3-dimensional analog of the hexagon. It shows up all over the place! You might enjoy these rhombic dodecahedral dice https://www.mathartfun.com/thedicelab.com/SpaceFillingDice.html https://www.mathartfun.com/thedicelab.com/SpaceFillingDice.h...
- DonHopkins 8y ago
  I'd enjoy reading some more character analysis of obscure polyhedra. The Dodecahedron was the most multifaceted character in The Phantom Tollbooth! https://www.shmoop.com/phantom-tollbooth/dodecahedron.html https://www.shmoop.com/phantom-tollbooth/dodecahedron.html http://teacherwifey.blogspot.com/2014/08/the-phantom-tollbooth-dodecahedron.html http://teacherwifey.blogspot.com/2014/08/the-phantom-tollboo...
- MrEldritch 8y ago
  It's "obscure" to me (and also my favorite) because I had never even heard of it before I tried to find out what the most natural 3-dimensional analog of the hexagon was. :)
  - jacobolus 8y ago
    Also see https://en.wikipedia.org/wiki/Kepler_conjecture https://en.wikipedia.org/wiki/Kepler_conjecture

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grey-area 8y ago

Is there any way to keep the objects spinning? It'd be nice if you gave them a flick and then they kept spinning under their own inertia.