In 3d quantum gravity, Planck's constant, the Planck length and the cosmological constant control the lack of (co)-commutativity of quantities like angular momenta, momenta and postion coordinates. I will explain this statement, using the quantum groups which arise in the 3d quantum gravity but avoiding technical details. The non-commutative structures in 3d quantum gravity are quite different from those in the deformed version of special relativity desribed by the kappa-Poincare group, but can be related to the latter by an operation called semi-dualisation. I will explain this operation, and make comments on its possible physical significance. The talk is based on joint work with Shahn Majid.