Foldable system, which is placeable in a daylight opening of an inner space of a building, for example in a window frame of a window pane between an inner space of a building and the outdoor environment, wherein the system comprises a foldable honeycomb body comprising an open honeycomb having honeycomb cells, e.g. wherein the honeycomb cells are diamond shaped, which honeycomb cells are permeable for a gas, e.g. for air, wherein a longitudinal axis of each of the honeycomb cells is perpendicular to the daylight opening, and wherein the honeycomb cells are open in a direction of the longitudinal axis when the system is arranged in the daylight opening in an unfolded configuration thereof, wherein the system further comprises a frame in which the foldable honeycomb body and a bar are arranged, wherein the foldable honeycomb body is only connected to the frame at a folding side of the frame, wherein the frame is placeable in the daylight opening of the inner space, and wherein the foldable honeycomb body - opposite to the folding side - is connected to the bar, which bar is moveable in the frame in opposed unfolding and folding directions between the folding side of the frame and a bar side of the frame, wherein the bar side is opposite to the folding side of the frame, wherein the frame comprises knife shaped connection elements at the folding side, which connection elements connect the frame with the foldable honeycomb body, which connection elements, preferably, each have a height that at least corresponds with half of a size of a honeycomb cell in the unfolding direction, wherein each honeycomb cell is connected at the folding side of the frame to an end point of one of said connection elements of the frame, and wherein the bar comprises knife shaped connection elements that connect the bar with the foldable honeycomb body, wherein the connection elements of the bar each with an end point thereof are connected with honeycomb cells of the foldable honeycomb body, wherein the honeycomb cells are adapted to close when the bar is moved in the folding direction from the bar side to the folding side of the frame by means of the connection elements, and wherein the honeycomb cells are adapted to open when the bar is moved in an unfolding direction from the folding side to the bar side of the frame, wherein, preferably, in a completely unfolded configuration, the bar lies against the bar side of the frame. wherein the system comprises a foldable honeycomb body comprising an open honeycomb having honeycomb cells, e.g. wherein the honeycomb cells are diamond shaped, which honeycomb cells are permeable for a gas, e.g. for air, wherein a longitudinal axis of each of the honeycomb cells is perpendicular to the daylight opening, and wherein the honeycomb cells are open in a direction of the longitudinal axis when the system is arranged in the daylight opening in an unfolded configuration thereof, wherein the system further comprises a frame in which the foldable honeycomb body and a bar are arranged, wherein the foldable honeycomb body is only connected to the frame at a folding side of the frame, wherein the frame is placeable in the daylight opening of the inner space, and wherein the foldable honeycomb body - opposite to the folding side - is connected to the bar, which bar is moveable in the frame in opposed unfolding and folding directions between the folding side of the frame and a bar side of the frame, wherein the bar side is opposite to the folding side of the frame, - is connected to the bar, which bar is moveable in the frame in opposed unfolding and folding directions between the folding side of the frame and a bar side of the frame, wherein the bar side is opposite to the folding side of the frame, wherein the frame comprises knife shaped connection elements at the folding side, which connection elements connect the frame with the foldable honeycomb body, which connection elements, preferably, each have a height that at least corresponds with half of a size of a honeycomb cell in the unfolding direction, wherein each honeycomb cell is connected at the folding side of the frame to an end point of one of said connection elements of the frame, and wherein the bar comprises knife shaped connection elements that connect the bar with the foldable honeycomb body, wherein the connection elements of the bar each with an end point thereof are connected with honeycomb cells of the foldable honeycomb body, wherein the honeycomb cells are adapted to close when the bar is moved in the folding direction from the bar side to the folding side of the frame by means of the connection elements, and wherein the honeycomb cells are adapted to open when the bar is moved in an unfolding direction from the folding side to the bar side of the frame, wherein, preferably, in a completely unfolded configuration, the bar lies against the bar side of the frame.