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He means turn the circle of fifths 180 degrees. In other words, move the chord up a tritone (six half-steps).

The drawing looks like a circle of half steps, not a circle of fifths.

It seems that the article would be clearer if the 180 degree rotation were to put F# at the top of the drawing.

Yes, good observation. Why would that help, though? No matter what's at the top, you're turning the whole thing halfway around.