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.