support knob 15 to attach the radiant mat grid tile to the underlying surface or sub flooring leaving the screw head or other attachment means below the recess 16 the upper surface of each tile contains a plurality of tube cradles 12 each tube cradle 12 is next to one or more weight bearing support knobs each weight bearing support knob 15 adjacent to a tube cradle 12 having an indented undercut notch in its surface on each side 14 adjacent to each tube cradle so as to allow tubing to snap into each tube cradle 12 thereby creating a truss to stiffen the radiant mat grid tile 9 limiting lateral flex in the preferred embodiment the tile is square but any polygonal shape can be used the desired plurality of radiant mat grid tiles 9 are placed on the floor ceiling roof and or walls and the multiple radiant mat grid 9 tiles are then snapped together along their perimeter by inserting the male knobs 10 into the adjacent female knobs 11 by stepping on or otherwise forcing the mating of the male and female knobs along the perimeter of each radiant mat grid tile 9 to create a contiguous matrix covering the desired portion of the floor wall or ceiling area to be radiantly heated or cooled after the desired entire floor wall or ceiling area to be radiantly heated or cooled is covered by the matrix a tube installation layout is configured and can be marked on the mat grid surface the tubing is then snapped into the matrix along the cradle and tube guides 12 and held securely in place by the.