A tile assembly for a diamond patterned roof, for installation on a roof extending in a plane inclined downwardly from the roof line, the tile assembly comprising:
- two, left and right center tiles, each tile having a generally diamond shaped repeating pattern each pattern having a main surface disposed in a plane nearly parallel to the roof plane and having upper and lower vertical apices spaced along an axis perpendicular to the roof line and left and right lateral apices spaced along an axis parallel to said roof line, wherein each pattern has six sides in a plan view and the main surface is flat throughout;
- each pattern having two upper flanges extending peripherally directly from the pattern main surface between its upper apex and its lateral apices, each upper flange extending upwardly and outwardly at an obtuse angle in a first direction from the main surface and having an outer edge parallel to the main surface and a transition plane extending between the outer edge and the main surface at the lateral extent of the pattern, the upper flange outer edges being joined at an upper flange apex;
- each pattern having two lower flanges extending peripherally directly from the pattern main surface between its lower apex and its lateral apices, each lower flange extending downwardly and outwardly at an obtuse angle in a second direction from the main surface and having an outer edge parallel to the main surface and a transition plane extending between the outer edge and the main surface at the lateral extent of the pattern, and the lower flange outer edges being joined at a lower flange apex;
- each pattern having two inflection planes, positioned at the lateral ends of each pattern, each inflection plane defined by the transition planes of the upper and lower flanges and an adjacent portion of the main surface, each inflection plane extending in a plane generally perpendicular to the main surface, wherein adjacent patterns within a tile are continuous to each other at their adjacent inflection planes, and may have a transition along the matching inflection planes;
- each patterns inflection planes end at the beginning of the inflection planes of the next lateral patterns on both sides or end where a transition is made between lateral patterns, with the transition being continuous to the abutting patterns, or the pattern ends at the lateral end of the tile;
- at each lateral end of the tile, the pattern inflection plane is also an inflection edge and includes the edge made by the transition planes of the upper and lower flanges and the adjoining main surface edge, an upper tile having the same configuration as each of said center tiles and that is positioned with two of its lower flanges of a pattern overlapping the two adjacent upper flanges of two center tiles;
- and a lower tile having the same configuration as each of the center tiles and that is positioned with two of its upper flanges of a pattern underlying the two adjacent lower flanges of two center tiles.