The most common group of transforms applied to objects are termed the Euclidean group of " isometries ", which are distance-preserving transformations in space commonly referred to as two-dimensional or three-dimensional (i.e., in plane geometry or solid geometry Euclidean spaces). These isometries consist of reflections, rotations, translations, and combinations of these basic operations. Under an isometric transformation, a geometric object is said to be symmetric if, after transformation, the object is indistinguishable from the object before the transformation. A geometric object is typically symmetric only under a subset or " subgroup " of all isometries. The kinds of isometry subgroups are described below, followed by other kinds of transform groups, and by the types of object invariance that are possible in geometry.