A floating floor assembled from an array of interconnected subunits, each of which includes a stone, ceramic or porcelain tile and a one-piece polymeric plastic substrate to which the stone, ceramic, or porcelain tile is bonded. Each substrate is injection molded from certain polyolefin polymers and incorporates the interlock structure and certain other features of the modular sports tiles of U.S. Pat. No. 4,930,286. The substrates of the present invention, however, differ in that each substrate incorporates a vertical stabilization system, the plastic support grid is formed by three sets of mutually intersecting walls, with each set being angularly offset from the other two by 120 degrees, and each substrate is sized to precisely fit a stone, ceramic or porcelain tile, which is accurately positioned by tile locator tabs on a pair of intersecting sides of the substrate.