It is well-known that Einstein gravity is kinematic in 3 dimension; i.e. Riemann is entirely written in terms of Ricci. The question is, can we universalise this property for all odd dimensions by properly defining analogues of Riemann and Ricci? The answer is yes, and it uniquely picks out the pure Lovelock (the Lagrangian has only one Nth order term) gravity for higher dimensions from all the possible theories including the Einstein theory itself. In the centenary year of GR, a theory which was purely driven by a principle, let’s pay tribute to that spirit by once again invoking a principle to show us the way in higher dimensions.