To separate into two parts, to classify into two classes, or to categorize into two categories.
The apostolical benediction dichotomizes all good things into grace and peace.
To exhibit as a half disk.
If the moon was a perfectly smooth sphere […] the place when she was dichotomized, […] would depend upon the sun's distance from the earth.
From Ancient Greek διχότομος (dikhótomos) + -ize.
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