An Aperiodic Monotile (2023)(cs.uwaterloo.ca) |
An Aperiodic Monotile (2023)(cs.uwaterloo.ca) |
I did a write up with some app you can play with a while ago:
And people say that mathematical research has no practical applications
Seriously, though, I think the implications for mineralogy are interesting.
Because both the hats and spectres are basically subset of triangular grid. Penrose tilings are subset of regular grid, too. Can we get rid of these underlaying regular grids.
Oh, from https://en.wikipedia.org/wiki/Fullerene:
"A closed fullerene with sphere-like shell must have at least some cycles that are pentagons or heptagons. More precisely, if all the faces have 5 or 6 sides, it follows from Euler's polyhedron formula, V−E+F=2 (where V, E, F are the numbers of vertices, edges, and faces), that V must be even, and that there must be exactly 12 pentagons and V/2−10 hexagons. "
So I'm not sure.