Abstract: A high-rise building comprises an exterior wall and a sheath, which is spaced in front of said wall. Vertically extending flow channels are provided between said wall and said sheath and are open at their bottom and top and may be used to supply air to and from the interior of said building and to air-condition the interior of said building. To permit an effective control of the conditions of the ambient air adjoining said sheath, each of said flow passages communicates with the ambient air adjoining said sheath through a plurality of vertically spaced apart intake openings distributed throughout the height of said sheath.