Three mutually orthogonal pairs of Helmholtz coils can be used to produce a fairly uniform magnetic field of arbitrary direction within a certain volume, and/or to null/cancel an external field (e.g. Earth's) to make a nearly field-free region.
In this answer to my question Why is there a large wooden ball on Mariner 3's magnetometer? I link to the NASA video MAVEN Magnetometer which includes some clips of the MAVEN spacecraft's three-axis fluxgate magnetometer being tested in a large workspace surrounded by the standard three pairs of Helmholtz coils.
However, when I look closely I can see another six coils, smaller in diameter and at larger distances. I've annotated a screen shot below to make this clearer.
Is there a name for this 12-coil configuration? Do the extra coils improve the uniformity within the center, or extend the useful size of the uniform area, or both, or neither?
If possible a link to the math is appreciated, but mostly I'd like to know if this is an established technique and what it's called.
I've done my best to indicate the primary three pairs and at least some of the secondary coils separately. I think one or two have been removed for access - so things can be wheeled in and out of the test volume.