Flat? The word was “smooth.” A ball.
That is one way of counting atoms; another way would be to create a cylinder. What makes a disc disc-y? A certain proportion between its dimensions?
For silicon, a particular isotope would be needed in order to pin down the precision satisfactorily.
They called the sphere smooth at the beginning of the article and flat at the end of it. A centrifuge was used to separate isotopes, so the sphere would be exceptionally pure.
http://www.nist.gov/pml/si-redef/kg_new_silicon.cfm