The superstructure (30) is releasably connectable with the tooth root implant (10) and a conical socket is provided in the head of the tooth root implant and below in the superstructure. The adapter (20) comprises two insert cones extending away from one another, which can be fitted in a releasable seat with the conical socket. Both insert cones are connected to one another by a transition piece which widens from the extension of the upper insert cone to the extension of the lower insert cone. The upper insert cone of the superstructure adapter (20) lies to its main axis in the range: 78 deg < alpha < 10 deg The cone angle ( beta ) of its lower insert cone to its main axis in the range: 1.5 < beta < 4 deg
