The word pendeloque essentially means "pendant" and was originally used not to describe a specific gemstone cut, but to describe any crystal that was fashioned so as to be hung, perhaps from a thread, chain or wire. The pendeloque is splendidly described in Thomas Blount's 1656 Glossographia, one of the first dictionaries:
Pendiloches: (Fr.) jags, danglings, or things that hang danglingly; with jewellers they are the lowest part of jewels, which hang in that manner."
Pendeloque and Briolette
There has historically been some confusion between the pendeloque and the briolette, although the use of the word briolette to describe diamonds appears much later, in the 19th century. In the 17th century, the word pendeloque was in common use in France and used to describe pendants, whether made of diamond or of other crystal. It was used at least as early as 1669  to describe both cut diamonds and also crystals hanging from chandeliers.
Although the term pendeloque was definitely used (in French) to describe diamonds in the latter part of the 17th century, it is thought that pendeloque or quasi-pendeloque diamonds may even have been created by Lodewyk (Louis) van Berquem, a Flemish cutter and polisher of the 15th century  although this is controversial.
Van Berquem, who made several advancements to the art of gemstone cutting, is said to have discovered in 1458 that diamonds could be cut by their own dust - however there are a few inconclusive references to diamond dust being used to polish crystals from India, some centuries before this. 
Van Berquem is thought by some to have cut the famous Florentine Diamond, a now-lost 137.27 carat yellow diamond that once belonged to the Medici family.  The Florentine Diamond, an irregular, intricate nine-sided gem of 126 facets, was (according to one of the legends surrounding its origin) cut by Lodewyk van Berken for Charles the Bold, Duke of Burgundy, some time before 1476.  It is considered by some to be a pendeloque or briolette cut, although others think of it as a variety of Double Rose Cut. 
In the 17th century, pictures of pendeloque-cut diamonds, looking very similar to the modern briolette, were recorded by Tavernier, a famous traveller who brought them back from India at that time. These had points top and bottom, yet Tavernier called them pendeloques in his description of his travels, published in 1679. Prints of Tavernier's drawings of these stones still exist.
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