A cylindrical polymeric cover for an industrial roll includes a plurality of through holes and a plurality of blind drilled holes. The through holes and the blind drilled holes are arranged in a pattern in which: (a) the through holes are arranged in rows that define an oblique angle relative to a plane that is perpendicular to a longitudinal axis of the cover; (b) the through holes of one row are offset from the through holes of the adjacent row, with the offset between rows defining an angle of approximately 20-40 degrees; (c) the blind drilled holes are arranged in rows located between the rows of through holes; (d) the blind drilled holes of one row are offset slightly from the blind drilled holes of the adjacent row, with the offset between rows defining an angle similar to that defined by the through holes; and (e) each of the blind drilled holes is located at the substantial center of a triangle defined by the closest three through holes.