Template:Monohedral quadrilateral tiling series description

One of a series of monohedral quadrilateral tiling patterns – tilings of the plane that are composed of identical quadrilateral tiles (allowing mirror image tiles).

File names and tile colourings are as for the pentagonal tilings, see here, except that tile types work differently. Quadrilateral types are as follows. Type 1: square or rectangle; type 2: rhombus; type 3: parallelogram; type 4: kite; type 5: right trapezium; type 6: trapezium; type 9: three sides equal; type 10: two adjacent sides equal; type 11: two opposite sides equal. Type 0 is a special type for the tiling pattern that allows any quadrilateral at all. If multiple types are satisfied then only the lowest is listed. Unlike the pentagonal types, one type can be a subset of another, and the existence of a type does not necessarily imply the existence of a tiling pattern that allows any member of that type.