Apparatus for the geometric measurement of an object, comprising: - a base and comprising a carrier device arranged thereon for the object, - at least one reference object (18, 20) which is fixable in relation to the base and comprising - at least one optical and contactlessly configured distance measuring device, by means of which a distance between the stationary reference object (18, 20) and the surface (14a, 14b) of the object facing the reference object (18, 20) is determinable and a surface contour of the object in relation to the reference object (18, 20) is ascertainable, and comprising - an object holder having an upper side and a lower side, the object being fixable to said object holder, wherein the object holder is selectively arrangeable with a first orientation and with a second orientation on the carrier device, - wherein the distance measuring device and the object holder are movable relative to one another for the purposes of scanning the surface (14a, 14b) of the object and wherein the object holder in each case has a reference structure (108, 110) on the upper side thereof and on the lower side thereof, said reference structure corresponding to the relative movement between object holder and the distance measuring device, - a controller, by means of which the surfaces (14a, 14b) of the object which are provided lying opposite one another at the upper side and lower side of the object holder and scanned by means of the distance measuring device are assignable to one another by means of the upper and lower reference structures (108, 110) scanned with the object surfaces (14a, 14b) and at least the thickness of the object and/or a wedge error of the object is ascertainable from a reciprocal assignment of the first surface image and second surface image of the surfaces. - a base and comprising a carrier device arranged thereon for the object, - at least one reference object (18, 20) which is fixable in relation to the base and comprising - at least one optical and contactlessly configured distance measuring device, by means of which a distance between the stationary reference object (18, 20) and the surface (14a, 14b) of the object facing the reference object (18, 20) is determinable and a surface contour of the object in relation to the reference object (18, 20) is ascertainable, and comprising - an object holder having an upper side and a lower side, the object being fixable to said object holder, wherein the object holder is selectively arrangeable with a first orientation and with a second orientation on the carrier device, - wherein the distance measuring device and the object holder are movable relative to one another for the purposes of scanning the surface (14a, 14b) of the object and wherein the object holder in each case has a reference structure (108, 110) on the upper side thereof and on the lower side thereof, said reference structure corresponding to the relative movement between object holder and the distance measuring device, - a controller, by means of which the surfaces (14a, 14b) of the object which are provided lying opposite one another at the upper side and lower side of the object holder and scanned by means of the distance measuring device are assignable to one another by means of the upper and lower reference structures (108, 110) scanned with the object surfaces (14a, 14b) and at least the thickness of the object and/or a wedge error of the object is ascertainable from a reciprocal assignment of the first surface image and second surface image of the surfaces.