QuadSphere | Ruby implementation of the quadrilateralised spherical cube | 3D Animation library

I've been trying to optimise how I lookup the neighbors for the Quad Tree faces in my Quad Sphere's Top and Bottom faces with the rest of the faces. I've attempted several methods to determine neighbors, where the latest one improved the lookup speed, but I'm wondering if there is something better

Method 1:

Keep a lookup table of all users of all vertices used by all Quads and then, for each Quad, find any other Quads that aren't ancestors that share edge vertices with the original Quad (minus the corner vertices because these are shared by multiple, non-neighbors). This works great for low numbers of subdivisions and vertices, but as each of these increases, the performance becomes much worse. See example here of this implementation: https://github.com/bicarbon8/QuadSphere/blob/master/Assets/Scripts/QuadVertMap.cs#L104

Method 2:

Keep a lookup table of all Quads at each Level of subdivision, indexed by level and then for each Quad, find any other Quads at either the same level or one level less (parents level) that aren't ancestors and check their edge vertices to see if they match with the original Quad's edge vertices. This works better than Method 1, but still starts to suffer if you get too deep in the levels of subdivision. This looks like the following code snippet: