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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
by 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 agoUnfortunately 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 agoI'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 agoIt'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 agoAlso see https://en.wikipedia.org/wiki/Kepler_conjecture https://en.wikipedia.org/wiki/Kepler_conjecture