C6, a minor third lower
The A6 tuning's open strings hold A, C#, E and F#. Those four notes are an A6 chord and an F#m7 at once, exactly as C6's C, E, G and A are both C6 and Am7. Sit Strings files A6 beside C6, under Hawaiian and swing playing.
The retune from C6 is the smallest on this site. Strings 1, 3 and 5 stay where C6 has them, on E, A and E, and the other three each move a single semitone: strings 2 and 6 up from C to C#, string 4 down from G to F#. No string travels further than that.
Reading the tables
The first table compares each string with C6, string 1, the highest, first. The second lists every chord type a straight bar or a slant spells in either tuning. A6 spells the same eight types as C6. The voicings differ, because the strings are arranged differently: the bar finds each chord at its own positions in each tuning.
Which A6
More than one six-string row is called A6. This page publishes C# E F# A C# E, low string first, the row two independent sources print. Another row starts on A and moves C6's own string pattern down a minor third; it rings as the same chord, with the strings in a different order.