An edge can be of a shape in a plane while a rim suggests a three dimensional object with a defined outer portion.
In geometry and topology "edge" has a definition which is very precise. "rim" haa no such specific determination.
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The radius is from the centre to the rim of a circle.
Two corners make up an edge.
A side is basically a geometrical shape; an edge is where two sides meet.
A side is basically a geometric shape; and edge is where two sides met.
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