For any set of regular polygons, it's possible to find edge length that allows to fit these polygons around a vertex in either spherical, Euclidean (for edge $0$), or hyperbolic plane. If we disregard the Euclidean case, how can I find sets that share the same edge length?
I know of two such pairs: $(3,10,3,10)$ and $(4,5,4,5)$, and $(4,10,4,10)$ and $(5,6,5,6)$. In both cases, two polygons add up to straight angle, so a vertex containing those four types of polygons shares the same edge length, which allows for various hybrid tilings.
Are there other solutions?