Relativity, as introduced by Einstein, is regarded as one of the most important revolutions in the history of physics. Nevertheless, the observation of direct outcomes of this theory on mundane objects is impossible because they can only be witnessed when relative velocities close the speed of light are involved. These effects are so counterintuitive and contradicting with our daily understanding of space and time that physics students find it hard to learn Special Relativity beyond mathematical equations and to understand the deep implications of the theory. Although we cannot travel at the speed of light for real, Virtual Reality makes it possible to experiment the effects of relativity in a 3D immersive environment. Our project is a framework designed to merge advanced 3D graphics with Virtual Reality interfaces in order to create an appropriate environment to study and learn relativity as well as to develop some intuition of the relativistic effects and the quadri-dimensional reality of space-time. In this paper, we focus on designing and implementing an easy-to-use game-like application : a carom billiard. Our implementation includes relativistic effects in an innovative graphical rendering engine and a non-Newtonian physics engine to treat the collisions. The innovation of our approach lies in the ability i) to render in real-time several relativistic objects, each moving with a different velocity vector (contrary to what was achieved in previous works), ii) to allow for interactions between objects, and iii) to enable the user to interact with the objects and modify the scene. To achieve this, we implement the 4D nature of space-time directly at the heart of the rendering engine, and develop an algorithm allowing to access non-simultaneous past events that are visible to the observers at their specific locations and at a given instant of their proper time. We explain how to retrieve the collision event between the pucks and the cushions of the billiard game and we show several counterintuitive results for very fast pucks. The effectiveness of the approach is demonstrated with snapshots of videos where several independent objects travel at velocities close to the speed of light, c.