This paper discusses and illustrates seven of the most interesting and beautiful curved Islamic star patterns, found either on historic monuments in Egypt and Syria or illustrated in Bourgoin's 1879 book, entitled Arabic Geometrical Pattern and Design [1], or both. The patterns — some considered masterpieces from the Mamluk period — were found on bronze or wooden doors or carved wooden minbars and are comprised of circular arcs, alone or in combination with line segments. Many of these curved patterns also have analogous “twins” constructed only of line segments. We present plausible Euclidean constructions of three of the patterns, which may all be categorized as belonging to the p4m, p6m or cmm crystallographic groups.