Housing for an electrical machine having - a cooling region, in which a plurality of cooling fins for guiding a coolant flow are arranged on an outer face of a housing wall, - a coolant supply region which adjoins the cooling region on a first side of the cooling region and which has at least one duct for supplying the coolant flow to the cooling fins of the cooling region and - a coolant discharge region which adjoins the cooling region on a second side of the cooling region opposite the first side and which has at least one duct for discharging the coolant flow from the cooling fins of the cooling region, wherein - at least one recess is arranged in the interior space of the housing for guiding a coolant flow inside the housing, wherein - the at least one recess extends in an axial direction along the housing and wherein - the at least one recess is introduced into the housing wall and serves to guide an interior cooling circuit, characterised in that - the housing in the coolant supply region has a rectangular cross-section, wherein in the interior space of the housing in the coolant supply region a duct for supplying the coolant flow is arranged in each of the corners, wherein the respective duct guides the coolant flow to the cooling fins in the cooling region of the housing, - the housing in the coolant discharge region has a rectangular cross-section, wherein in the interior space of the housing in the coolant discharge region a duct for discharging the coolant flow is arranged in each of the corners and - the rectangular cross-section in the coolant supply region and in the coolant discharge region has the same external dimensions as the housing in the cooling region. - a cooling region, in which a plurality of cooling fins for guiding a coolant flow are arranged on an outer face of a housing wall, - a coolant supply region which adjoins the cooling region on a first side of the cooling region and which has at least one duct for supplying the coolant flow to the cooling fins of the cooling region and - a coolant discharge region which adjoins the cooling region on a second side of the cooling region opposite the first side and which has at least one duct for discharging the coolant flow from the cooling fins of the cooling region, wherein - at least one recess is arranged in the interior space of the housing for guiding a coolant flow inside the housing, wherein - the at least one recess extends in an axial direction along the housing and wherein - the at least one recess is introduced into the housing wall and serves to guide an interior cooling circuit, characterised in that - the housing in the coolant supply region has a rectangular cross-section, wherein in the interior space of the housing in the coolant supply region a duct for supplying the coolant flow is arranged in each of the corners, wherein the respective duct guides the coolant flow to the cooling fins in the cooling region of the housing, - the housing in the coolant discharge region has a rectangular cross-section, wherein in the interior space of the housing in the coolant discharge region a duct for discharging the coolant flow is arranged in each of the corners and - the rectangular cross-section in the coolant supply region and in the coolant discharge region has the same external dimensions as the housing in the cooling region.