Cairo Tiling
The Cairo tiling is a tiling of the plane by non-regular pentagons which is dual to the snub square tiling.
Free Modular Lattice on 3 Generators
This is the free modular lattice on 3 generators, as drawn by Jesse McKeown. First discovered by Dedekind in 1900, this structure turns out to have an interesting connection to 8-dimensional Euclidean space.