Euclidean space Euclidean group The Euclidean group is the isometry group of -dimensional Euclidean space , #m/def/geo/affine consisting of transformations that preserve Euclidean distance. It is equivalent to the semidirect product of the appropriate real orthogonal group with the translation group Related groups The relativistic counterpart is the Poincaré group #state/develop | #lang/en | #SemBr