# How to differentiate similar clusters in the mcsqs output in ATAT?

Consider the following bestcorr.out file:

2   0.866025    -0.000000   0.000000    -0.000000
2   0.866025    0.000000    -0.000000   0.000000
2   0.866025    -0.000000   0.000000    -0.000000
2   1.000000    -0.000000   0.000000    -0.000000
2   1.000000    -0.000000   -0.000000   -0.000000
2   1.000000    -0.000000   0.000000    -0.000000
2   1.414214    -0.000000   0.000000    -0.000000
2   1.414214    -0.000000   -0.000000   -0.000000
2   1.414214    0.006944    0.000000    0.006944
Objective_function= -1.630678


This was for a BCC ternary SQS. Let's consider the $$1^{st}$$ nearest neighbour (NN) pairs. There are three of them; how do we differentiate among them?

Here is the part of clusters.out that concerns these pairs:

4
0.86603
2
1.50000 0.50000 0.50000 1 0
1.00000 -0.00000 1.00000 1 0

8
0.86603
2
1.50000 0.50000 0.50000 1 1
1.00000 -0.00000 1.00000 1 0

4
0.86603
2
1.50000 0.50000 0.50000 1 1
1.00000 -0.00000 1.00000 1 1


corrdump manual page: https://www.brown.edu/Departments/Engineering/Labs/avdw/atat/manual/node35.html

Why are there $$3$$ different kinds of pairs with the same distance? At first, I thought in a ternary alloy it could mean $$AB$$, $$BC$$, and $$CA$$ pairs. $$A$$, $$B$$, and $$C$$ being constituent atoms. Now that I think of it, that doesn't make sense else it would apply to triangles and higher clusters as well but it doesn't.