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PROFESSOR CIMA: Now there are so-called "families" of directions.
So if I go back to my-- Draw it big enough so you can see it.
In a cubic lattice, if you think about it, this direction, this direction,
this direction, basically all these directions, this direction like this,
look the same. It's a cubic lattice, right?
I could just flip this on its side. And basically you'd all get the same thing.
So we call these families, with this funny bracket like this.
There are the set. And turns out there six independent ones,
six of them. Basically all the different pairs of directions.
I got one here, one there. I guess I didn't do that one.
Six of them. And the same's true with the 111 for example.
Remember, the [111] was the body diagonal, the purple one.
There's a set of all those too. Turns out there's eight independent ones.
So the family is going to be, well [111]... This is basically all the permutations.
And the reason why you didn't have 8 here is because negative
of 0 is still 0. So that wouldn't be independent.
Here with three 1's, you get eight different permutations.
Question. OK.
Oh sorry. STUDENT: So how do you define family?
Like how-- PROFESSOR CIMA: Well, in a cubic crystal these
directions all share the same symmetry.
So if I'm looking along any one of these directions and I were to take a
picture looking down this direction, it would look the same.