What are the diamonds on Indian head pennies?

Actually, there are 4 diamonds that are part of the head dress ribbon. If you look closely at the ribbon running down the side behind the ear, you will see them imbedded in the ribbon. These are usually the first part of the design to wear off a circulated Indian cent, hence the description accompanying many of them that are for sale. The terms 4 diamonds, 3 diamonds, etc. refer to the quality of the coin.

AnswerThere are no diamond shapes in the design.

If you are referring to the small indentations around the rim of the coin they are called "denticles" and are simply a part of the artistic choice of the designer and engraver.