inner edge 36 with middle region 24 and fourth radius 44 formed by joining inner edge 36 with bottom region 32 here preferably fourth radius 44 is larger than third radius 42 logically third radius 42 is the same length as second radius 28 and first radius 26 is the same length as fourth radius 42 the difference is that the curve is inverted for first and second radius as opposed to third and fourth radius the inverted curve allows for the mating mechanism of the female receiving portion to the male protruding portion preferably the tiles have the male protruding portion and female receiving portion all along the edges to interlock with other tiles however it is contemplated that there are pieces where at least one edge of the tile does not have any male protruding portion or female receiving portion for instance tiles that are placed on the outer edge against a straight floor do not need to have connectors in fig3 a 3 b and 3 c a modular floor covering system 100 comprises the joining of tiles 10 by interlocking male protruding portions 12 of the individual tile to female receiving portions 14 of the adjoining tile fig3 b and fig3 c specifically depicts the joining of corner pieces 50 corner pieces in general comprises corner male protruding portions 58 mating corner female receiving portion 56 the corner male protruding portion generally is at the adjacent side of the female receiving portion similar to male protruding portion 12 and female protruding portion 14 there is corner cap 54 and corner stem 52 the corner cap and stem are different than the other cap and.