is shown in fig4 more specifically adjacent undulating rings 30 and 32 are illustrated each of these rings has an undulating preferably sinusoidal shape with alternating high and low peaks for example in ring 30 alternating high peaks 34 exist between low peaks 36 between peaks 34 and 36 are valleys 35 the height is defined as the distance from valleys 35 to peaks 34 the crossties 38 connect ring 30 to ring 32 crossties 38 are optional as ring 30 can be connected directly to ring 32 without them crossties can connect peaks to peaks valley to valley or at least one peak or one valley to another location on the next ring ring 32 has alternating high peaks 40 and low peaks 42 the high peaks 40 of ring 32 are juxtaposed against the low peaks 36 of ring 30 similarly the low peaks 42 of ring 32 are juxtaposed against the high peaks 34 of ring 30 the result of this construction is that the oblong openings 44 get smaller as adjacent rings such as 30 and 32 in a typical stent s get nested into each other the minimum length of opening 44 is less than the combined height of peaks 34 and 42 including the material fig5 illustrates the resultant shape of the opening 44 after radial expansion of the rings such as 30 and 32 which make up the stent s fig5 can be compared to fig2 to illustrate that the typical opening in the stent s of the preferred embodiment of the present invention is smaller than the large oblong openings 24 which necessarily arise when rings such as 10 and 12 are aligned adjacent peak 14 to peak.