An abradable structure (10) for a turbomachine (40) that is designed to be at least partially deformed and / or at least partially abraded by at least one abrading element (44, 47) of the turbomachine (40) during operation thereof; the at least one abradable structure (10) being formed at least regionally of structural elements (12, 14, 16, 18) that have a respective polygonal cross section (20, 22) that is oriented in a rub direction (X_A) of the abradable structure (10). The structural elements (12, 14, 16, 18) have a greater extent (Xh, Xr) in the rub direction (X_A) than in a direction of the abradable structure (10) that is orthogonal to the rub direction (X_A). Other aspects of the present invention relate to a turbomachine (40) having an abradable structure (10), as well as to a method for manufacturing an abradable structure (10).