A regular tetrahedron (better known as a three-sided pyramid) with three numbers on each face. This odd die is best thrown by tossing it a few inches into the air with something of a spin to it; when it lands, the number on each face that's right-side up (on most d4s the numbers will be on the bottom edge, though on some they're found on the top point instead) is the result. Naturally, on the vast majority of d4s, the unmodified result of such a roll is a natural number from 1 to 4. In the various incarnations of D&D and AD&D, common uses for d4s include wizard hit dice and dagger damage dice.

Don't sit on one of these. Especially not a razor-edged one.

Crystal Caste put out a special "d4". Why the quotes, you ask? Because the die has 12 sides. However, only 4 of them are numbered. These four sides are arranged in an elongated cube shape, with small, pyramid-like sides on the long ends of the cube, so small that gravity forces the cube to land on one of the bigger, numbered sides. Quite ingenious: Mabye not as random as a regular d4, but this freak show of dice rolls quite well, and looks damn spiffy, too.