What is the rectangular shape given to a gemstone by cutting and polishing?

I think what you are referring to is known as the "Baguette Cut". Some other cuts are:

  • Solitaire Cut- a cut rounded at the top, which is sometimes, as the name implies, a solitaire stone, but is sometimes surrounded by other diamonds of the same, or different cuts
  • Princess Cut - a square cut
  • Marquis Cut - a diamond shaped stone, much like the diamond shape in the diamond suit of a deck of cards
  • Round Cut - round, as the name implies, and usually clustered together with other diamonds of the same cut.

Additionally, you may be thinking of an emerald cut which is a rectangular shape. There is also the cushion cut, which is a cross between an oval and an emerald cut.