The third side of a coin is called the edge. The edge runs the entire circumference of the coin between the heads side, call the obverse, and the tails side, called the reverse. It is literally the third side of the coin.
People confuse the edge of the coin with the rim of the coin. The rim of a coin is found on either the obverse or reverse side. The rim is the raised part of the coin that encircles the diameter of the coin. A coin can have two rims. The edge is the side where the reeding, or grooving, is found on quarters and dimes. Coins have only one edge.