A method and apparatus for releasbly attaching flexible abrasive disks to a flat-surfaced platen that floats in three-point abrading contact with three rigid equal-height flat-surfaced rotable fixed-position workpiece spindles that are mounted on a precision-flat abrading machine base where the spindle surfaces are in a common plane that is co-planar with the base surface. The three spindles are positioned to form a triangle of platen supports where the rotational-centers of each of the spindles are positioned at the center of the annular width of the platen abrading surface. Flat surfaced workpieces are attached to the spindles and the rotating floating-platen abrasive surface contacts all three rotating workpieces to perform single-sided abrading. The platen abrasive can be re-reflattened by attaching equal-thickness abrasive disks to the three spindles that are rotated while in abrading contact with the rotating platen abrasive. There is no wear of the abrasive-disk protected platen surface.