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				NullAshton said: 
Just use depleted uranium. Volia, cheap radiation shielding!  
			
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 Hmm not sure about the cheap part, especial given the quantitiie invovled.
Someone mentiond  story referrencing tranparent shup hulls, the only one i can think of was "ringworld Engineers" by Larry Niven. and the race that built/sold them physically resembled the cue cappa.
As for meterrilas strong enought oto build such a structure. well as someone suggested reguarding Buckyballs i just read a recent article Regaring Carbon nanotubes.  They have in th lab at least, created nanotube sheets at rates up 7 Meters per minute.  Carbon nanotube cables would have the strength necessary to build a space elevator. 
which there has been a revived intrest in, theres now a robotics contest for build a climber.