This image shows the "base" or fundamental roots for A3 (red balls) and the fundamental weights (blue balls).

Each fundamental weight is perpendicular to two of the three fundamental roots, and projects orthogonally

to one-half of the third fundamental root. The two fundamental roots in the horizontal plane are perpendicular

to each other; each fundamental root in the horizontal plane is at a 120-degree angle to the third

fundamental root. From this we obtain the Dynkin diagram for A3: three nodes with a single bond between

the first and second and between the second and third (for roots at 120 degrees), and no bond between the

first and third (for the two perpendicular roots).