Hypercuboidal renormalization in spin foam quantum gravity

In this article we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion letter, in which the existence of a fixed point in the truncated RG flow for the model was reported. Here we repeat the analysis with various modifications, and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.