A three‐dimensional space‐time geometry of relativistic particles is constructed within the framework of the little groups of the Poincaré group. Since the little group for a massive particle is the three‐dimensional rotation group, its relevant geometry is a sphere. For massless particles and massive particles in the infinite‐momentum limit, it is shown that the geometry is that of a cylinder and a two‐dimensional plane. The geometry of a massive particle continuously becomes that of a massless particle as the momentum/mass becomes large. The geometry of relativistic extended particles is also considered. It is shown that the cylindrical geometry leads to the concept of gauge transformations, while the two‐dimensional Euclidean geometry leads to a deeper understanding of the Lorentz condition.

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