The buyer was Laurence Graff, the billionaire diamond dealer whose clients run to other newly minted billionaires, and in short order its new owner made a series of startling decisions about the stone. First, he had it recut, reducing it from 35.52 to just over 31 carats, to eliminate the chips and “bruises” inevitable in a stone of its age but also to improve its clarity, brilliance and grade. Then he renamed it the Wittelsbach-Graff and struck an agreement with the Smithsonian Institution in Washington to display it.

Image The Wittelsbach diamond (shown in 2008 before recutting) was part of the dowry for the Infanta Margarita Teresa. Credit... Christie's

Late this month, it will go on view alongside the legendary Hope, a larger stone but a slightly more drab one, and yet a rock whose allure remains potent enough to have drawn five million visitors to the national collection last year.

“The Hope Diamond is by far our most popular object,” Jeffrey E. Post, curator of the National Gem and Mineral Collection at the Smithsonian, said last week, comparable in its drawing power to the Mona Lisa at the Louvre. The reasons, Dr. Post added, are as faceted and prismatic as the stone itself: “Gems form in the earth, so every gemstone has an incredible natural history. But they also made it to the surface of the earth somehow, were found and cut and set.”

Visitors to the Smithsonian who will soon have the rare opportunity to share in the Wittelsbach’s tale will also be venturing into the midst of a controversy about the gem. By recutting it, some critics suggest, Mr. Graff has not so much improved it as altered it out of all recognition. “That stone has a pedigree that is incomparable,” Daniela Mascetti, a senior global specialist in jewelry at Sotheby’s, said by phone from London. “The provenance of a gem is important in ways that are not true of other things. With the Wittelsbach blue, you knew how it came into existence and in a rather exciting way. You know who has worn it, what kinds of historical events it has gone through and what social upheavals it was present for.”

Like the Hope, the Wittelsbach is thought to have originated in India, at the Golconda mines, and was also likely to have been brought to the West by Jean-Baptiste Tavernier, the 17th-century traveler and trader. In 1664, King Philip IV of Spain gave it to the Infanta Margarita Teresa to mark her engagement to Leopold I of Austria; in 1722, the diamond passed to the Wittelsbachs, members of Bavaria’s ruling house. In the upheaval after World War I, Bavaria became a republic and the crown jewels of the House of Wittelsbach were dispersed. Except for the exhibition preview for the Christie’s auction the stone was last seen in public at the 1958 Brussels World’s Fair.