A universal abrasive sheet is provided for a sanding or polishing machine and includes segments defined by weakened regions that allow portions of the universal abrasive sheet to be removed in order to adapt the abrasive sheet to alternative platent configurations. Each of the different configurations of the universal abrasive sheet can be provided with an individualized tip portion which can be separated from a body portion and either repositioned or replaced in order to change the working point of the tip portion when it becomes worn out.