Another Dice Question

The die with the fewest number of sides is the tetrahedron. People often think of it as a pyramid with a triangular base. The three sides are triangles, and so is the base. So there are four identical sides.

Two tetrahedral dice

How many ways can a tetrahedral die be numbered, using the numbers 1, 2, 3, 4 exactly one time each?

Same Dice

Two dice are “the same” if they can be rotated until their numbers match up exactly. For example, if you take a tetrahedral die, and place it with the 1 on the base, the and the 3 to your left, the 4 to your right, and the 2 behind, that’s the same as a die with 1 on the base, 4 on the left, 3 behind, and 2 on the right (it’s just been rotated).

Different numberings

How many different numberings are possible?

The way mentioned above is one possibility. How many altogether.

Previous

The same question, but for a cube, with 6 square faces, is here. And some solutions for the cube are here.