I have run a simple script that numerically computes edge lengths of various hyperbolic tessellations and compares them. It seems that if you fit two squares and two 2n-gons to each vertex (combination (4.4.2n.2n) or (4.2n.4.2n)), the edge length will be exactly one half of edge for combination (n.n.2n.2n.2n.2n).
Is this true generally? Why?