"....This is why in some traditions - ie. Adderbury & Headington, where there are complex hand movements, the handkerchiefs (or Wavers - as Diane says - although I also have never heard that term!) are held on diagonal corners....."
Never seen a Hanky, or a Waver, held by anything other than the corner. Now if you hold a Hanky by the corner, it doesn't really have much choice as to being "diagonal"
In closing I would say that only "snotty" people would call "ankies", "wavers".
JohnB who uses "sticks" when he dances.