Could 2 dimensional objects fill a 3 dimensional space?

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Imagine if we had an infinite number of 2d objects, could they fill a 3d volume? even if there is an infinite number of them?
 

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There are no 2d objects in physics, and not an infinite amount of anything. In mathematics, it depends on the type of infinity you mean.
 
Mathematically there are space filling curves - physically no.
 
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