# How do I find Miller indices for a plane whose intercepts are fractions of the lattice constant?

[I'm talking with respect to cubic lattices alone.]

For instance, if a plane has $$x,y,z$$ intercepts $$a/2,a/2,a/2$$ (where $$a$$ is the lattice constant) the miller index would be $$[2\space2\space2]$$. The book I'm referring to says that for fractional intercepts, the indices do not have to be reduced to the smallest whole numbers(hence $$[2\space2\space2]$$).

But, miller indices are supposed to represent a set of parallel planes and I can't think of any other plane with the index $$[2\space2\space2]$$ Then I saw this:

The image(3rd row, 3rd image) shows the set of $$[2\space2\space2]$$ planes. I'm guessing that one of them has intercepts $$a/2,a/2,a/2$$. What are the intercepts of the other planes, and how are they all $$[2\space2\space2]$$?

Or, if my method of calculation is wrong, how else do I calculate miller indices for fractional intercepts?

PS: I've only just started to learn this concept, so it's possible that my understanding of miller indices is fundamentally flawed.

$$d=\frac{a}{\sqrt{h²+k²+l²}}$$