In some cases, hexagons are used in percolation. Why do we use hexagons in percolation?



Why do we use hexagons in percolation?
Site percolation on the triangular lattice (or, equivalently, face percolation on the hexagonal lattice) is the only case for which conformal invariance of percolation at criticality has been [proven](http://www.sciencedirect.com/science/article/pii/S0764444201019917). This has to do with very special combinatorial properties of the lattice. For a detailed explanation of this, see [this paper](https://arxiv.org/abs/0708.3908) by Vincent Beffara.


