Connection piece for connecting four pipe sections, in particular of an air distribution system, wherein the connection piece has four connection openings in which a respective end of one of the four pipe sections is fixable in a fluid-tight manner, wherein each of the four connection openings has a substantially oval-shaped cross section, which has two axes of symmetry (X, Y) orthogonal to one another, the width B of which cross section as measured along its first axis of symmetry being greater than the height H of said cross section as measured along its second axis of symmetry, wherein a) the connection piece forms a channel passing configuration, in which a first channel section of the connection piece and a second channel section of the connection piece are arranged separate from each other in a fluid-tight manner, passing each other and crossing each other in a channel crossing region; b) the first channel section and the second channel section in the channel crossing region each have an increased width B* and a reduced height H* and each have a substantially oval-shaped cross section, which has two axes of symmetry (X*, Y*) orthogonal to one another, its width B* as measured along its first axis of symmetry X* is greater than the width B, and its height H* as measured along its second axis of symmetry Y* is smaller than the height H; c) the connection piece is formed as one piece or as two pieces of two substantially identical channel parts (36, 37), which each have a first connection opening (31, 32) and a second connection opening (33, 34), wherein each of the two channel parts (36, 37) between the two connection openings (31, 32, respectively 33, 34) have an axial section with increased width and decreased height, its width B* as measured along its first axis of symmetry X* is greater than the width B, and its height H* as measured along its second axis of symmetry Y* is smaller than the height H, in other words B*>B>H>H*; and d) four fittings extend between the first channel part and the second channel part to fix the connection piece to a base. a) the connection piece forms a channel passing configuration, in which a first channel section of the connection piece and a second channel section of the connection piece are arranged separate from each other in a fluid-tight manner, passing each other and crossing each other in a channel crossing region; b) the first channel section and the second channel section in the channel crossing region each have an increased width B* and a reduced height H* and each have a substantially oval-shaped cross section, which has two axes of symmetry (X*, Y*) orthogonal to one another, its width B* as measured along its first axis of symmetry X* is greater than the width B, and its height H* as measured along its second axis of symmetry Y* is smaller than the height H; c) the connection piece is formed as one piece or as two pieces of two substantially identical channel parts (36, 37), which each have a first connection opening (31, 32) and a second connection opening (33, 34), wherein each of the two channel parts (36, 37) between the two connection openings (31, 32, respectively 33, 34) have an axial section with increased width and decreased height, its width B* as measured along its first axis of symmetry X* is greater than the width B, and its height H* as measured along its second axis of symmetry Y* is smaller than the height H, in other words B*>B>H>H*; and d) four fittings extend between the first channel part and the second channel part to fix the connection piece to a base.