A stabilization device for bones or vertebrae is provided comprising: a rod (20, 20') having a rod portion with a rod axis (L) and with a number (n) of distinct external surfaces (21a, 21b, ...21i; 21a', 21 b', ...21i') that are arranged in an n-fold rotationally symmetrical manner around the rod axis (L), a bone anchoring device (1, 1', 100) including a receiving part (3, 105) comprising a channel for receiving the rod portion, wherein the receiving part includes a rod support (8, 8', 173); a fixation member (40, 40'', 400) for fixing the rod in the channel; wherein the rod support (8, 8', 173) and the fixation member (4,4'', 400) each comprise at least one contact surface (8a, 8b; 8a', 8b'; 173a, 173b) that is configured to contact an external surface of the rod portion, and wherein saidcontact surfaces (8a, 8b; 8a', 8b'; 173a, 173b) and said external surfaces (21a, 21 b, ...21i; 21a', 21b', ...21i') are configured and arranged to clamp the rod portion along at least three surface areas.