Dice Chirality

Normal six sided dice (d6) which obey the rule of having opposite sides add to seven come in two distinct varieties. To show this observe that if we place the 1 and the 2 on a die then they must be adjacent since if they weren't then they must be opposite to each other which can't happen because they don't sum to seven. Therefore we can label them arbitrarily like this:

This fixes the faces opposite them to make the sums get to seven like this:

However, we are yet to fix the 3 and the 4. They actually work either way around:

These two dice are said to have different chiralities, which is a word that you might recognise from chemistry where molecular structures can come with a different handedness, producing very different properties. It is also an important concept in biology with many asymmetrical animals such as snails coming in either a left handed (shelled) or right handed variety. This is exactly the same with these dice:

The right handed varieties are the ones used in the West. Almost every dice you have ever used has been of that type. However, in China, Japan and Korea the prevailing type is of the left handed variety. If you have ever noticed a dice with a large red pip for the 1 and the four also inexplicably red then you were using a Chinese dice:

The different layouts of pips in the East (top) and West (bottom). Notice the 2 pips.

The different dice.

One place you may have experienced Eastern dice is in Christmas Crackers. Typically they are manufactured in China at conform to their standards.