In this talk I will present recent results on the renormalization of the

4D Euclidean EPRL spin foam model, which is restricted to be

"cuboid-shaped". To this end I will review the construction of this

restricted model, which is defined on a hypercubic 2-complex and thus

called "quantum cuboids". In order to define a renormalization group

flow I need to represent the same (physical) process, e.g. a transition,

on different discretisations, which is done by relating the states on

the boundary of the foams via embedding maps. In this restricted model,

this essentially reduces to relating coarse to fine cuboids via a

geometrical embedding map. Hence I define a renormalized amplitude,

whose properties are studied by numerically computing expectation values

of simple observables. The observables are used to project the

renormalized amplitude down to the original model resulting in a

renormalization group flow. Remarkably, this flow shows indications for

a phase transition and an UV-attractive fixed point. Furthermore it

appears that diffeomorphism symmetry might be restored on this fixed point.

This talk is based on work in collaboration with Benjamin Bahr,

arXiv:1605.07649, arXiv:1508.07961 and work in progress.