noun
rim is applied to the edge of a circular or curved surface; brim refers to the inner rim at the top of a cup, glass, bowl, etc. or to the projecting rim of a hat; brink refers to the edge at the top of a steep slope; border refers to the boundary of a surface and may imply the limiting line itself or the part of the surface immediately adjacent to it; margin implies a bordering strip more or less clearly defined by some distinguishing feature the margin of a printed page; edge refers to the limiting line itself or the terminating line at the sharp convergence of two surfaces the edge of a box: all of these terms have figurative application the rim of consciousness, a mind filled to the brim, the brink of disaster, the border of good taste, a margin of error, an edge on one's appetite
See rim in Webster's New World Roget's A-Z Thesaurus II
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