# How can the 'crystal cleavage' of apatite have a four-digit number?

On Wikipedia's page for apatite, the crystal cleavage is listed as [0001] or [0101], which I assume are Miller indices....

But how can there be four numbers/digits instead of two, like there usually are?

Putting the first three axes into the same plane means the intercept designations on these axes must be dependent on each other; in fact those three numbers should add up to zero. Thus $$[1010]$$ is not correct; it should be $$[10(-1)0]$$ or using the more common notation for a negative index, $$[10\overline10]$$. As shown in the above illustration, physically this corresponds to the lateral face of a hexagonal prism.