A2 lattice
Whenever we have a simply-laced Dynkin diagram, integer linear combinations of our unit vectors form a lattice with remarkable properties.
For example, the so-called A2 Dynkin diagram:
gives this lattice:
I created the Dynkin diagram here, and I hereby release it into the public domain. The picture of the A2 lattice was created by Jim Belk and put into the public domain on Wikicommons.