Here's something that I found out recently.

In hyperbolic plane, we can put, say, pentagons and triangles together in (5,5,5,3) tiling. But that tiling is not uniform -- you can't make it so each vertex looks the same.

Surprisingly, it turns out that when you double this tiling (six pentagons and two triangles per vertex, arranged as (5,5,5,3,5,5,5,3)), there IS a way to make it uniform. The key is that two (5,5,5,3) "halves" that form a vertex do not have to be identical. So, does that mean that there exists an "almost-uniform" version of (5,5,5,3) that is still periodic, just has two distinct classes of vertices instead of one class?