Synonyms for border

These nouns refer to the line or narrow area that marks the outside limit of something such as a surface. Border refers either to the boundary line (a fence along the border of the property) or to the area immediately inside (a frame with a wide border). Margin is a border of more or less precisely definable width: the margin of the page.
Edge refers to the bounding line formed by the continuous convergence of two surfaces: sat on the edge of the chair.
Verge is an extreme terminating line or edge: the sun's afterglow on the verge of the horizon.
Figuratively it indicates a point at which something is likely to begin or to happen: an explorer on the verge of a great discovery.
Brink denotes the edge of a steep place: stood on the brink of the cliff.
In an extended sense it indicates the likelihood or imminence of a sudden change: on the brink of falling in love.
Rim most often denotes the edge of something circular or curved: a crack in the rim of the lens.
Brim applies to the upper edge or inner side of the rim of something shaped like a basin: lava issuing from the brim of the crater.