to cut away the same size isoceles triangle from each of four interconnected master flooring assemblies at the point of their alignment this leaves a square opening rotated 45 degrees from the master tray substrate in a conventional tile system a smaller medallion tile would be set into the opening with a corner of the medallion tile laying in the grout line between two master tiles the medallion tray substrate provides a unique way of placing a medallion tile into the modular interlocked master tile assemblies as described earlier the medallion tray substrate is similar to the master tray substrate in many ways the medallion tray substrate has optional vertical tray edges a tray surface a tray bottom an optional pad it may also have optional vertical setting pins the medallion tray substrate differs from the master tray substrate in that the medallion tray substrate does not have interlocking connections configured like the master tray substrate the medallion tray substrate has at least two radial arms that protrude from the tray side in the radial direction measured from the geometric center of the radial arms the geometric center of the radial arms is the point from which the arms radiate and the point around which the angles separating the radial arms are measured the geometric center of the radial arms may be the geometric center of the medallion tray substrate but it does not have to be for example if one wished to offset the medallion design from the grout lines of the master tray substrate one would place the geometric center of the radial arms well away from the geometric center of the medallion tray substrate the radial arm is designed to slide in between the grout line.