An exemplary support structure has an auto-adaptable surface. The exemplary support structure comprises a base; an assembly of distinct, adjacent contacts; and an assembly of platforms of a common level forming a common tier, each platform being linked to the base by an articulation. The platforms have multiple branches, each branch supporting a contact, and the contacts and the platforms have three degrees of freedom in rotation. Thus, the contacts are linked to the base such that they are mobile with respect to each other and with respect to the base to form the auto-adaptable support surface.