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Opposite of concave . A geometric shape is convex if all its edges point outwards. That is no part of it curves or faces inwards. If a shape is convex, a line segment drawn between any two points on the shape will always lie inside the shape. The figure above is a convex pentagon. No part of it is caved in and any line segment, such as the red one shown, linking two points on it always lies inside the shape. See also Concave definition.
from The Century Dictionary and Cyclopedia. Curved, as a line or surface, in the manner of a circle or sphere when viewed from some point without it; curved away from the point of view; hence, bounded by such a line or surface: as, a convex mirror.