  The amorphous four-dimensional differentiable manifold possesses a  high degree of symmetry. Because of its homogeneity, all points are  alike; there are no objective geometric properties that enable one to distinguish one point from another. This full homogeneity or symmetry of space must be described by its group of automorphisms,  the one-to-one mappings of the point field onto itself which leave  all relations of objective significance between points undisturbed.  If a geometric object \(F\), that is a point set with a definite  relational structure is given, then those automorphisms of space that leave \(F\) invariant, constitute a group and this group describes exactly the symmetry which \(F\) possesses. For instance, to use  an example by Weyl (1938b) (see also Weyl (1949a, 72–73) and  Weyl (1952)), if  \(R(p_{1},p_{2},p_{3})\) is a ternary relation that asserts  \(p_{1},p_{2},p_{3}\) lie on a straight line, then we require that any three points,  satisfying this relation \(R\), are mapped by an automorphism into three other points  \(p_{1}',p_{2}',p_{3}'\), fulfilling the same relation. 