A stabilization device for bones or vertebrae includes a rod having a rod axis and a plurality of distinct external surfaces that extend parallel to the rod axis, such that for a cross-section of the rod, the distinct external surfaces are arranged at respective angles relative to one another around the rod axis, a bone anchoring device including a receiving part having a channel for receiving the rod and a contact surface for supporting the rod, and a fixation member with a contact surface for fixing the rod in the channel. When the rod is fixed in the channel with the fixation member, the contact surfaces of the receiving part and the fixation member together form surface portions that are shaped to correspond to at least three of the distinct external surfaces, such that the rod is clamped along the at least three distinct external surfaces.