This is a set of images of the dice that make up my collection of all the possible variations of spots on dice. It includes the standard dice with the diagonal twos in the left two columns and the twos horizontal and vertical in the right two columns
The dice were placed in front of a three element corner mirror resting on the 1 face so the 2, 3, and 6 faces were showing. These are the faces that can be rotated from the traditional 000 orientations. If you have faith that the opposite sides add up to seven, you can figure out where all the faces are. Being skeptical myself, I imaged the set so the "back" faces could be seen in the mirrors. Note that the only face which cannot be seen is the 1 face that each die is resting on.
LH 000 RH ..................LH HV Twos .........................................RH HV Twos ........
LH 000 RH == LH 000 RH
LH 006 RH == LH 006 RH
LH 030 RH == LH 030 RH
LH 036 RH == LH 036 RH
LH 200 RH == LH 200 RH
LH 206 RH == LH 206 RH
LH 230 RH == LH 230 RH
LH 236 RH == LH 236 RH
LH 000 RH == Illegal > <Illegal resting on Five Face
The Illegal Dice opposite sides do not all add up to seven. The opposite sides are 1:2, 5:6, and 3:4.
The 2HV dice were all purchased from the Dollar Tree. My son, Paul, saw them and purchased one set for me. After I looked at the set and found five types of 2HV dice, I went back th the store and purchased all they had on hand (Total=ten sets of 6 dice = 60 dice, each 2 blue, 2 green, 2 orange.). The 60 dice contained all the possible 2HV combinations plus the illegal die. I expect that the dice spots were painted with a stencil or silk screen, one side at a time, manually rotating the dice between paintings. The manual rotation is what leads to the high variability.
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