The disclosure is of a cigarette or like packet of composite foil, with lateral end flaps separated from inner neighboring longitudinal end flaps but continuously connected with outer longitudinal end flaps and folded in between the inner and outer end flaps with the formation of overlying triangular lappets. For making and filling the packet there is an apparatus with winding mandrels to roll the foil into a tube, and a turret having devices for filling the tube and forming it into a closed packet by folding end flaps.