NOVELTY - The method comprises: coaxially assembling a hollow casting cylinder (414) and a mask cylinder (412), where one of the casting cylinder and the mask cylinder has an inner diameter that is larger than an outer diameter of the other of the mask cylinder and the casting cylinder; inserting liquid polymer precursor in a space between the casting and mask cylinders; curing the liquid polymer precursor in the space to form a layer of cured polymer; removing the casting cylinder leaving the layer of cured polymer on a surface of the mask cylinder; and patterning a surface of the cured polymer.    USE - The method is useful for fabricating a cylindrical mask that is useful for lithographically forming a patterned substrate such as plastic film, metal film, thin glass sheet, glass panel and semiconductor wafer (all claimed) used in the micro-scale and nano-scale fabrication of solar cells, LEDs, integrated circuits, microelectromechanical system devices, architectural glass and information displays.    ADVANTAGE - The method is capable of preventing a seam from being transmitted to the substrate when the cylindrical mask is used to repeatably pattern the substrate thus economically avoiding stitching errors in the pattern when patterning the polymer.    DETAILED DESCRIPTION - The method comprises: coaxially assembling a hollow casting cylinder (414) and a mask cylinder (412), where one of the casting cylinder and the mask cylinder has an inner diameter that is larger than an outer diameter of the other of the mask cylinder and the casting cylinder; inserting liquid polymer precursor in a space between the casting cylinder and the mask cylinder; curing the liquid polymer precursor in the space between the casting cylinder and the mask cylinder to form a layer of cured polymer; removing the casting cylinder leaving the layer of cured polymer on a surface of the mask cylinder; and patterning a surface of the cured polymer. The coaxially assembling step includes using an assembly apparatus having a first plate (402a), a second plate (402b) and a pin (406). The pin is configured to retain the first plate and the second plate together at opposing ends of the casting cylinder and the mask cylinder. The step of inserting liquid polymer comprises pouring the liquid polymer through holes in the first plate. The first plate has a first groove aligned with the mask cylinder and a second groove aligned with the casting cylinder. The second plate has a first groove aligned with the mask cylinder and a second groove aligned with the casting cylinder. The casting cylinder has an inside diameter that is larger than an outside diameter of the mask cylinder. The casting cylinder has a patterned inner surface. The step of patterning the polymer comprises using the patterned inner surface to transfer a pattern on the patterned inner surface to a surface of the polymer. The method further comprises: patterning an inner surface of the casting cylinder before the step of coaxially assembling; depositing liquid polymer on the inner surface of the casting cylinder before the coaxially assembling step; and curing the polymer on the inner surface of the casting cylinder before the coaxially assembling step such that the inserting liquid polymer precursor comprises inserting the liquid polymer precursor in a space between the outer surface of the mask cylinder and the inner surface of the cured polymer. The step of patterning the inner surface of the casting cylinder comprises: performing an anodization process to create a nanoporous surface; depositing self-assembling nanoparticles on the inner surface of the casting cylinder; etching the inner surface of the casting cylinder using the nanoparticles as an etch mask; removing the nanoparticles; successively imprinting the inner surface of the casting cylinder with a smaller area master mask having a pattern; performing nanoimprint lithography, nanocontact lithography and photolithography; and patterning an outer surface of the polymer after the removing step. The nanoparticles are nanospheres. The step of patterning the outer surface comprises using a mask cylinder having a patterned outer surface such that a pattern of the patterned outer surface is transferred to the inner surface of the polymer during the method of fabricating a cylindrical mask. INDEPENDENT CLAIMS are included for:    (1) a cylindrical mask;    (2) a lithography method;    (3) a substrate;    (4) a rotatable mask;    (5) a method for making a rotatable mask;    (6) a method of patterning a substrate;    (7) a method for forming a master mold for a cylindrical lithography mask;    (8) a master mold for a cylindrical photomask;    (9) a method for forming a master mold for a cylindrical photomask; and    (10) a cylindrical master mold assembly.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of an assembly apparatus.    First plate (402a)    Second plate (402b)    Pin (406)    Mask cylinder (412)    Hollow casting cylinder. (414)