Looking for opposing face pairs is the easy method, and works on most of the questions (I think 6 of the 9.) If all the opposing pairs are the same, there are

Looking for opposing face pairs is the easy method, and works on most of the questions (I think 6 of the 9.) If all the opposing pairs are the same, there are two more ways to distinguish. One is the placement of the symbols relative to each other; the chirality of the whole object. For an example, think of a six-sided die. Position it so that the 6 is on top and 2 is towards you. The left and right faces will be the 3 and 4, in either order, creating two distinct possibilities. The other remaining distinction is the orientation of the symbols on each face. Continuing the die example, with the 6 on top and the 2 towards you, the 2 pips can have either of two diagonal orientations. Orientation creates a possibility space of 2^N * 4^M where N is the number of sides with 2-way orientation distinguishability and M is the number of sides with 4-way distinguishability. On a normal die, N = 3 since the 2, 3, and 6 are 2-way orientable, and M = 0. Some of the questions here have M > 0, specifically the arrows and hearts. (I'm ignoring cases where rotating the whole cube creates duplicate possibilities. Consider one side with an arrow and 5 blank sides; although the arrow has 4 orientations, they are not distinguishable. I'm also ignoring the possibility of rotating a symbol in non-90° increments.)