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FIELD OF THE INVENTION 
     The invention relates to a roofing, for flat or arched roofs, made with molded synthetic-resin components shaped so as to permit rapid and stable assembly, effective protection from the infiltration of rain water, thermal and acoustic insulation and other purposes and advantages, which will be clear from the following text. It is also important to note that—among other things—the covering hereof is particularly resistant over time to weather and other conditions, offers substantial chromatic stability (for aesthetic or other purposes) and is environmentally-friendly, as the roofing is made of entirely recyclable material. The tiles removed from demolished buildings can also be easily used again. 
     The roofing includes tiles and devices for fastening said tiles to a block or beam and batten frame supporting structure. 
     The tiles can be made of stiff, molded synthetic resin and comprise: along the edges which, when laid, are essentially perpendicular to the maximum slope line, an upper continuous contoured ridge along the upper edge and a lower continuous contoured ridge along the lower edge; and along the edges which, when laid, are essentially parallel to the maximum slope line, contours which are complementary in the partial overlap between said edges of contiguous tiles to make labyrinth seals which will carry off rain water towards the tiles of the row below. 
     According to this invention, said ridges are step-shaped to engage, when laid, with horizontal continuity, a row of tiles below with the row of tiles above. Furthermore, said anchoring, devices include; a through hole in one of the ridges and a slot in the other ridge to fasten two tiles from contiguous rows that partially overlap along the ridges to an underlying supporting structure with a screw device. 
     Advantageously, said continuous ridges are square step-shaped, which also allows limited relative sloping by limited relative play. 
     The screw holes are formed next to the lower edge whose lower ridge overlaps the upper ridge of a tile below presenting two slots. Said slots can be formed in enlargements of the ridge of said upper edge. 
     That one of the aforesaid complementary labyrinth contours, which is underneath the other when laid, and forms ducts on the upper, i.e. dorsal, surface, can end—downstream—with a stepped recess to facilitate water carry-off onto the tile below. 
     The roofing can include ridge caps shaped like inverted gutters which can present overlapping profiles to form carry-off duct labyrinths and, along each of the longitudinal edges, a flexible lip suitable for adapting to the slope of the corresponding roof pitch and for being anchored to the tiles on which it rests when laid. 
     The roofing can include half tiles for completing each horizontal row of adjacent tiles, to be arranged alternately at one end and at the opposite end in contiguous rows of tiles, so that the tiles of one row are staggered with respect to those of the contiguous row; which half tiles can also be produced by cutting a tile. 
     In a possible configuration, the plate of the tile forms a “bent tile” contour with external and internal arched terminal edges which engage, when laid, with those of the plates of contiguous rows. 
     Some tiles can be made of clear material, such as polycarbonate or similar, to create skylights simply by fitting the clear tiles in specific areas of the roof. 
     The invention will be better understood with the following description and accompanying drawing, illustrating a practical, nonrestrictive example of the invention. 
     The various features of novelty which characterize the invention are pointed out with particularity in the claims annexed to and forming a part of this disclosure. For a better understanding of the invention, its operating advantages and specific objects attained by its uses, reference is made to the accompanying drawings and descriptive matter in which preferred embodiments of the invention are illustrated. 
     FIG. 1 illustrates a perspective view of a roofing, with parts removed; 
     FIG. 2 illustrates a set of tiles, of which only one is in solid lines, to illustrate rows of staggered tiles on a roofing; 
     FIGS. 3 and 4 illustrate perspective views of a tile, from above and from below; 
     FIGS. 5,  6  and  7  illustrate local sections marked V—V, VI—VI and VII—VII in FIG. 2; 
     FIGS. 8 and 9 illustrate local sections, marked VIII—VIII and IX—IX in FIG. 2; 
     FIGS. 10 and 11 illustrate local sections marked X—X and XI—XI in FIG. 2; 
     FIG. 12 illustrates a partial perspective view of a tile along the side forming the labyrinth; 
     FIG. 13 illustrates a plan view of a portion of FIG.  12  and of a contiguous, partially sectioned tile; 
     FIGS. 14,  15 ,  16  and  17  illustrate elements for forming a ridge between two pitches, in views and sections marked XIV—XIV in FIG. 1, XV—XV in FIG. 16, XVI—XVI and XVII—XVII in FIG. 14, on various scales; 
     FIGS. 18,  19 , and  20  illustrate tiles of reduced dimensions in views from above and from below and in cross section according to line XX—XX in FIG. 19; and 
     FIG. 21 is a perspective view of a modified embodiment of the tile. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     As illustrated in the accompanying drawing, the tile  1  consists of a plate  3 , with relatively limited thickness and a substantially rectangular shape, presenting an upper edge  3 A and lower edge  3 B when laid with the inclination due to the slope of the roof.  3 C and  3 E, on the other hand, indicate the edges parallel to the maximum slope line. Plate  3  is relatively thin and reinforced by means of a ribbing parallel to edges  3 C and  3 E, which forms channels  3 F on the dorsal, i.e. the external, surface when laid. The channels start at a limited distance from upper edge  3 A and drain along lower edge  3 B to eliminate rain water onto the dorsal surface of the tiles below, i.e. downstream with respect to the maximum slope and direction of rain water flow shown by arrows f 1 . A continuous upper step-shaped contoured ridge  5  is formed on the surface of the tile along the upper edge  3 A. Ridge  5  can form an approximate right angle. A lower continuous downward ridge  7  is formed along the lower edge  3 B and extends towards the lower, or palmar, surface of the tile, with a profile substantially complementary to that of ridge  5 . The two ridges  5  and  7  engage and couple as illustrated, in particular, in FIGS. 5,  8 ,  9 ,  10  and  11 , with limited play to allow, if required, limited angular adaptation between successive tiles along the maximum slope line. This ensures easy coupling between successive tiles along the maximum slope line and also makes it possible to follow any curves in the roofing. 
     Edges  3 C and  3 E, which once laid slope with the maximum roof slope, present complementary contours which—in the partial overlapping between said edges  3 C and  3 E of contiguous tiles of a horizontal row of tiles—form labyrinth seals which will carry off water towards the tiles of the row below. For this purpose, edge  3 C of the tile which is designed to remain underneath in the overlapping between contiguous tiles, presents two longitudinal ridges  3 G and  3 H defining two ducts, while the edge  3 E, above in the overlapping between contiguous tiles, presents two longitudinal ridges  3 K and  3 L which interpose between the two ridges  3 G and  3 H, forming the aforesaid labyrinth (see, in particular, FIGS.  6  and  7 ). The edge  3 E of each tile may be completed with a limited ridge  3 E 1  which covers the connection between the two tiles, for nearly the entire connection, with the exception of a small section towards the upper edge  3 A and ridge  5 . The continuous ridge  5  presents a notch  9  at the corner between edge  3 C and edge  3 A, which reduces the step profile. A recess  11  is provided in ridge  7  at the corner between edge  3 C and edge  3 B, where the ducts formed by longitudinal ridges  3 G and  3 H lead. This step-shaped recess  11  facilitates rain water downflow along the ducts formed by said ridges  3 G and  3 H. Furthermore, a step  13  is created at edge  3 E (see specifically FIGS. 2,  3  and  4 ); the step is shaped to house the residual part  9  of the contoured ridge  5  where step  9  is created on the contiguous tile. An indent  15 , on the other hand, is formed in the convergence between edge  3 E and edge  3 B to allow edges  3 C and  3 E of contiguous tiles to overlap and maintain continuity between contoured ridges  7  of the contiguous tile in a row. This ensures that, during assembly, an adequate passage is created between recess  11  and indent  15  for draining water from the ducts formed by ridges  3 G and  3 H to the tiles on the row below. An angular projection  11 A on recess  11  stabilises the position between tiles where recess  15  is arranged (see specifically FIGS.  12  and  13 ). 
     Tiles  1  are made of injection molded thermoplastic resin. The resin may be either coloured or clear (e.g. for manufacturing fixed skylights). These materials are totally recoverable and even repeatedly recyclable. 
     Anchoring of tiles to the roofing support structure S is done along horizontal edge  3 A of plate  3  of tile  1 . 
     The support structure S can consist of a block or a beam and rafter structure—with battens, where required—or other equivalent structures for this purpose, on which to arrange and anchor profiles  30 . These profiles can consist of wooden laths  18  horizontally anchored to structure S. Said laths  18  can take wood screws or similar. 
     The tiles  1  present linear ridges  20  and  20 A—on the lower face and along a lower reinforcement  5 A on ridge  5 —which are designed to rest on the horizontal laths  18  (or other supporting structure) so as to maintain an air circulation gap between tiles and laths  18 . Along side  3 A, the ridge  5  and the respective enlargement  5 A present enlargements  5 B, where through slots  24 , parallel to edge  3 A, are formed (also see FIG.  10 ). A hole  26 —with upper enlargement  26 A—is formed in each tile  1  next to ridge  7  and to lower edge  3 B. When assembled, a large screw  28  can be inserted in hole  26 ,  26 A of one tile and in slot  24  of the tile below to be fastened to lath  18 . This fastens the tiles  1  to laths  18 . A seal is placed under the head of screw  28  to prevent the infiltration of water. 
     Ridge  5  along edge  3 A of the tile presents two narrower areas  5 E for molding reasons. 
     Special linear ridges  30  can be formed on the upper face of each tile and along the reliefs to provide adequate resistance to prevent the feet of people accessing the roof for inspections, or other purposes, from slipping. 
     The roofing assembly is started from the eaves tiles which are arranged on the supporting structure and anchored with screws  28  to lath  18  near the eaves. The next row of tiles  1  is then laid over the first row of eaves tiles, engaging the two rows of tiles by coupling ridges  5  of the tiles of the row above with ridges  7  of the tiles of the first row, and so on. A slight slope variation can be attained between the tiles of one row and those of the contiguous row. With a single screw  28  for each tile the entire roofing can be secured. Interventions which may be required in time after assembly—for replacements or other purposes—are possible by removing a very limited number of screws  28 . The assembly operation is continued all the way to the ridge. 
     The tiles of the various successive rows can be staggered with respect to each other. Tiles presenting a horizontal dimension (i.e. distance between an edge corresponding to  3 C and an edge corresponding to  3 E) smaller than regular tiles can be used alternatively at the ends of successive rows. When tiles are arranged in a staggered fashion with respect to those of adjacent rows, tiles presenting a size equal to half the distance between edges  3 C and  3 E—as illustrated in FIGS.  18 - 20 —can be used. Alternatively, regular tiles can be cut in half along a middle line between edges  3 C and  3 E to obtain two “complementary” half tiles. An even roof covering will be produced, including along the maximum slope line at the ends of the roofing, by arranging the half tiles alternately at one end of one row and at the opposite end of a contiguous row. 
     The same tiles can be manufactured with inert filling material, selected to offer thermal and acoustic insulation. Furthermore, by using laths  18  of suitable height, the space between structure S and the tiles can be used to accommodate thermal and/or acoustic insulation material and/or channels or the like. 
     Ridge caps, generically indicated as  34  (see FIGS.  14 - 17 ), can be used to complete the roof along a ridge, specifically between opposite pitches presenting equal or different slopes. These ridge caps form an inverted “gutter” once fitted and are mutually engaged by the partially overlapping ends, due to the presence of arched edges  34 A which are inserted into arched ducts  34 B of the contiguous ridge cap, as clearly shown in the drawing. Ridge caps  34  are suitable for covering the tiles of the last upper row of each pitch by containing the upper ridges  5  of the tiles of said last rows, as shown by the section view in FIG.  14 . The ridge caps  34  are anchored by the longitudinal corners of caps  34  extending for at least the main portion of their development to form lips  36 , which are flexible, i.e. can be slanted variably by the reduction in thickness of fitting  38  between the sides of the ridge caps  34  and the lips  36 . As a result, the lips  36  can be adapted to practically any maximum slope line of roofing pitches and can be fastened to the tiles by means of rivets, screws, nailing or other. These lips  36  ensure the anchoring of ridge caps  34  without the risk of infiltration of rain water. Tightness can be ensured by the adherence of lips  36  to the tile, by the virtually waterproof nature of rivets  40 , or equivalent fasteners, and due to the fact that the ridges  5  of the tiles are contained inside the ridge caps. At the end, or at both ends, of the roof ridge, special ridge caps with ends such as  34 E, finished with a partition, instead of a simple side, form a duct such as  34 B. A similar side can be used also for all the other ridge caps. Ridge caps can be sawed like tiles. 
     FIG. 21 illustrates a modified tile for making roofs similar to those traditionally made with flat plain tiles and inverted-duct arched bent tiles. Part  101 , unique in this case, is similar to the tile described above but plate  103  of said tile is modified centrally to form “bent” contour  203 , with arched terminal edge  205  projected outwards at the end corresponding to ridge  105 , and arched terminal edge  207  projected inwards, at the end which corresponds to ridge  107 . When laid, edge  205  of the part  101  below is contained by edge  207  of the part  101  above. This forms “bent tile” contour lines  203  along the maximum slope lines. The contiguous parts  101  of successive rows are, in this configuration, aligned, rather than, as in the successive rows of tiles of the configuration illustrated in FIG. 1, staggered. The bent tiles  101  can similarly be laid with a limited curvature of the maximum slope line. 
     It will be understood that the drawing only illustrates an example provided for practical demonstration purposes of this invention only, as its forms and configurations can be modified without departing from the scope of the concept on which this invention is based. Any reference numbers included in the accompanying claims have the purpose of facilitating reading the claims with reference to the description and the drawing and. does not limit the scope of protection represented by the claims. 
     It is worth noting that the tile material can be coloured as required for aesthetic purposes. Clear material—such as polycarbonate—can be used for roofing which allows natural lighting of the interior.

Summary:
A tile made of stiff molded synthetic resin having edges which overlap when a plurality of tiles are assembled upon a roof and an upper continuous contoured ridge along the upper edge and a lower continuous contoured ridge along the lower edge. The upper and lower ridges being stepped shape to engage with horizontal continuity when a plurality of tiles are assembled upon a roof. A through hole is provided in the lower ridge which aligns with a slot in the upper ridge to allow a screw to pass therethrough fastening two contiguous rows of tiles to a supporting structure.