Battery module having: a plurality of battery cells , each comprising at least one first electrode and at least one second electrode , and a separator are positioned between the first electrode and the second electrode , and a battery cell housing , which comprises a first housing half and a second housing half , wherein the first housing half is electrically insulated from the second housing half and wherein the first electrode is electrically contact-connected to the first housing half and the second electrode is electrically contact-connected to the second housing half , wherein the first electrode and the second electrode are aligned in parallel with a bottom face or a top face of the battery cell , and wherein the bottom face and the top face of the battery cell housing are embodied in the form of a regular hexagon, and a battery module housing , which has side walls and a top face and a bottom face, wherein the battery cells are contact-connected both in the region of the bottom face and in the region of the top face of the battery module housing , wherein the battery cells are arranged spaced apart from one another in a horizontal plane so that a throughflow option in the form of temperature-control medium channels for a temperature-control medium is produced between the side faces of adjacent battery cells , as a result of which the temperature-control medium can flow along the side faces of the battery cells, wherein the battery module housing has a temperature-control medium inlet and a temperature-control medium outlet and wherein the temperature-control medium can flow through the battery module housing in the horizontal plane. a plurality of battery cells , each comprising at least one first electrode and at least one second electrode , and a separator are positioned between the first electrode and the second electrode , and a battery cell housing , which comprises a first housing half and a second housing half , wherein the first housing half is electrically insulated from the second housing half and wherein the first electrode is electrically contact-connected to the first housing half and the second electrode is electrically contact-connected to the second housing half , wherein the first electrode and the second electrode are aligned in parallel with a bottom face or a top face of the battery cell , and wherein the bottom face and the top face of the battery cell housing are embodied in the form of a regular hexagon, and a battery module housing , which has side walls and a top face and a bottom face, wherein the battery cells are contact-connected both in the region of the bottom face and in the region of the top face of the battery module housing , wherein the battery cells are arranged spaced apart from one another in a horizontal plane so that a throughflow option in the form of temperature-control medium channels for a temperature-control medium is produced between the side faces of adjacent battery cells , as a result of which the temperature-control medium can flow along the side faces of the battery cells, wherein the battery module housing has a temperature-control medium inlet and a temperature-control medium outlet and wherein the temperature-control medium can flow through the battery module housing in the horizontal plane. <EOS>