The invention relates to a high-pressure fuel pump for operating an internal combustion engine, having a pump housing (3) in which a pump camshaft (1) is supported and which is connected to at least two pump pistons (5a, 5b) via a polygonal configuration (4), said pistons being guided in a displaceable manner in associated pump cylinder heads (6a, 6b) that are placed on the pump housing (3), wherein the rotating movement of the pump camshaft (1) is converted to translational movements of the at least two pump pistons (5a, 5b) in order to suction off fuel from a low-pressure circuit, compress the fuel to high pressure, and to convey the same to a high pressure storage, wherein further a low-pressure unit (10) that accommodates the low-pressure circuit is attached to the pump housing (3).