A surface fine machining tool has a working medium carrier with a bottom side and a top side. Grooves extend from the top side to the bottom side completely through the working medium carrier and have a narrowed portion at the bottom side but do not narrow upwardly toward the top side. The working medium carrier is an injection-molded plastic part. Lamellas with a holding rim and a lamella body are inserted with the holding rim in the grooves. The lamella body extends downward away from the holding rim, passes through the narrowed portion, and extends away from the bottom side. The lamellas are uniformly distributed about the bottom side. The grooves have an open end at a carrier rim of the working medium carrier. The open end has a cross-section matching the groove cross-section. A cover is connected to the top side and covers grooves and holding rims.