The Lyte Jewel shown here is actually a enamelled gold bejewelled locket which once belonged to Thomas Lyte (1568-1638), a minor courtier in the court of King James I of England. He received it as a gift from his sovereign after commissioning an illuminated royal pedigree. The cover of the locket bears the letters "IR", Latin for Iacobus Rex. Underneath is a portrait miniature of the king.
Rectangular table cut diamonds surround the cover. Table cut diamonds resemble a bicone with its tip lopped off. This was the earliest form of diamond faceting. As you can see, some of the gems showed a little sparkle, others looked rather dull.
Before the 13th century, diamonds were simply polished smooth. This did nothing to enhance the gemstone's potential to disperse light but it did conserve carat weight. The Moghul Emperor Shah Jahan (builder of the Taj Mahal ) had such a domed diamond pendant which is now owned by Elizabeth Taylor. You can see a picture of it on my past mini-biographical post, "The Jewels and Jewelry Obsession of Shah Jahan".
The rose cut (originated in India) followed the table cut where the table was replaced with six triangular facets which improved the light dispersion. But it took the brilliant cut, first developed in the 17th century and called the Old Cut, with its 58 facets to really bring out the sparkle and fire of diamonds. The modern brilliant cut came along in 1919 and after considerable honing by both mathematical and empirical means, it has became the most popular cut style.
Watch this one minute video , a PBS/Nature overview of diamond cutting where in the end, it is the careful observation, skill and experience of the diamond cutter which determines how a faceted diamond turns out.
Picture Source
References
Hugh Tait (1986). Jewelry: 7000 years. British Museum.
Judith Crowe (2006). The Jeweler's Directory of Gemstones. Firefly Books Ltd.
Wikipedia : Diamond Cut
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The Beading Gem's Journal