And the third is the 100x100 tilings, takes 2 minutes and 4 seconds to render.
Every object in it is intersection with the bounding cylinder first, then union.


#declare one_piece =
union{
    box{
    <0.005, 0.005, 0>, <0.395, 0.395, 0.01>
    }
    cylinder{
    <0.02, 0, 0>, <0.38, 0, 0>, 1
    scale <1,0.18,0.02>
    translate <0, 0.2, 0.01>
    }
    pigment{
    rgb<0.4,0.6,0.6>
    }
}

#declare the_tiling =
union{
    #for(i, 0, 99)
        #for(j, 0, 99)
            intersection{
                object{
                one_piece
                translate <i*0.4, j*0.4, 0>
                }
                cylinder{
                <20,20,0>,<20,20,1>,19
                }
                cutaway_textures
            }
        #end
    #end
}


the_tiling

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