Dice Question

How many ways can a die be numbered, using the numbers 1, 2, 3, 4, 5, 6 exactly one time each?

(Some solutions posted here. Add your own!)

Same Dice

Two dice are “the same” if they can be rotated until their numbers match up exactly. For example, if you take a standard die, and place it with the 1 on top, the 6 will be on the bottom. If you rotate it so the 2 is in front, the 5 will be in back. And then you might notice the 4 is on the left, and the 3 is on the right. All standard dice are numbered this way.

Different numberings

How many different numberings are possible?

The standard die (mentioned above) is one possibility.

You could swap the 4 and the 3, and that would be a second numbering.

How many are there, altogether?