In heraldry, relating to the right side of a shield or coat of arms (as viewed by the shield's bearer, not the viewer).
From Latin 'dexter,' meaning right or on the right side. In heraldry, the term preserved the Latin meaning specifically because heraldic conventions maintained Latin terminology. The word has been used in English heraldry since the medieval period. It contrasts with 'sinister' (Latin for left).
Here's the trick: in heraldry, 'dexter' means the right side from the perspective of someone holding the shield—so it's the LEFT side from your perspective looking at it! Medieval heralds confused generations of people this way on purpose to keep their knowledge exclusive.
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