I can't remember found I came by these dice. (They may possibly have come from Christmas crackers.) Inside each of them is a heavy ball which helps them come to rest. As you can see from the die on the right, it is not entirely clear which of two numbers are uppermost. So if they were used competitively, no doubt there would be no end of argument between the players.
In fact there are 30 different ways in which the dots can be arranged on each die. The following (from Mathematische Basteleien) shows all 30:
In addition to there being 30 different ways in which the dots can be arranged on each die, as Mathematische Basteleien goes on to point out, each set of dots can be can be arranged in four ways (since each face can be rotated four quarter turns). Because of rotational symmetry, this doesn't affect the appearance of the 1, 4 and 5 - they look the same at each turn. However, for 2, 3 and 6 there will be two different appearances (since the 2 and 3 are on a diagonal and the dots of the 6 are arranged 2x3). That, by my reckoning, would make a total of 240 different dice, if the orientation of the dots was also taken into consideration.