and 4 has a generally pyramidical configuration with point 23 at the peak of the pyramid and points 43 47 51 at the base of the pyramid constant cross section portion 25 of the embodiment of fig3 and 4 includes an extension of cord 41 referencd in fig4 as 41a the embodiment of fig5 and 6 is similar to that of fig3 and 4 except that the leg further includes piles such as that shown at 57 driven through leg cords 45 49 and mat 19 into seabed 39 leg cords 45 49 of the embodiment of fig5 and 6 will ordinarily have a tubular configuration see e g the configurations of fig1 17 described infra so that piles can be driven therethrough using such piles rig 11 can be used as a battered leg fixed platform similar to fixed platforms already in use unlike a fixed platform a rig 11 using the leg of fig7 and 8 can be recovered and reused referring to the embodiment of fig7 and 8 variable cross section portion 21 includes truncated cone 61 having base 63 secured to platform 19 preferably one side of cone 61 is substantially vertical cone 61 may be made of steel plate reinforced by internal stiffening members shown in fig8 as dashed lines 64 cone 61 has a substantially circular opening at.