SI Unit: Mole
This sphere is made from a crystal of silicon-28, and used in the International Avogadro Project to determine the Bolzmann constant by essentially counting the number of atoms in a sphere. The more perfect the sphere—and the more perfect the crystal’s interior arrangement of atoms—the more accurate their count. The sphere and [optics] lab are at Germany’s Physikalisch-Technische Bundesanstalt, and were shown to me by Peter Becker, who says “Everything that has a spherical shape is somehow attractive for mankind."
Often this sphere has been called the world’s roundest object, but there are competing claims. Richard Davis at BIPM told me about two quartz-silicon spheres used as gyroscopes in NASA’s Gravity Probe B. According to NASA, if the 1.5” quartz spheres were the size of Earth, the tallest mountain would be 12 feet high. On the silicon-28 sphere, if Earth-sized, the tallest mountains would be either 9 or 16 feet. Whichever number you choose, Richard points out that when NASA's spheres are in orbit, the silicon-28 sphere is the roundest object on the planet.