What is the name of the four-dimensional geometry in special relativity?

The four-dimensional geometry of special relativity is called Minkowski spacetime.

It combines three spatial dimensions with time into a single four-dimensional mathematical model. Unlike ordinary Euclidean geometry, time does not behave like a fourth copy of length: the spacetime interval uses a metric with a different sign for the time component. That structure allows all inertial observers to agree on the interval between two events, even when they disagree about measured distances and durations.

Hermann Minkowski developed this geometric formulation from the work of Albert Einstein, Hendrik Lorentz, and Henri Poincaré. In his influential 1908 lecture, Minkowski argued that space and time should be treated together rather than as separate absolute entities. His framework made effects such as time dilation, length contraction, and the relativity of simultaneity easier to visualize and calculate.

Minkowski spacetime describes flat spacetime, meaning gravity and curvature are absent or negligible. General relativity extends the idea to curved spacetime, while each sufficiently small local region of a curved spacetime still resembles Minkowski space. Euclidean space is therefore a tempting but incorrect answer: it has four dimensions in some mathematical settings, but it is not the geometry of special relativity.