Tiles having a matrix of interconnected vaults on its underside surface provides space for flow of heated or conditioned air, passages for electrical service conduits and wiring, or passages for drainage. In particular, each tile may comprise a solid rigid body having a substantially planar upper surface and thickness substantially less than upper surface linear dimensions. The underside surface has a set of concavities forming a matrix of vaults bounded and interconnected by archways. Each archway is characterized by a rise dimension that is less than a span dimension. The matrix of vaults defines a set of pendentives at each vault corner whose load-bearing bases are all substantially coplanar with one another so as to contact a supporting subfloor. Edges of the tile body have corresponding alternating laterally projecting extensions and indentations for forming (with some desired leeway) mortise-and-tenon joints between adjacent tiles.

A system and method of removably attaching a flooring surface material to a subfloor. The subfloor may include a modular raised flooring system comprising a plurality of raised floor panels, and comprising a magnetic body, surface or underlayment material. The flooring surface material includes a magnetic attachment surface that holds the flooring surface material in place on the subfloor by magnetic attraction, but that allows removal for disassembly and/or replacement.

A modular decking system includes a plurality of modular components. Each component has a frame, a deck, a jack screw, and alignment blocks. The frame includes a pair of vertically disposed and offset boards banding the exterior periphery with internal cross members and block adjacent corners. The deck is a plurality of boards fitting within the offset boards of the frame's periphery. The screw jacks are located within the corner blocks. The alignment blocks affixed to the frame's periphery are used to position one modular component adjacent another modular component.