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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.
The geometric definition of a vertex is a point in a geometric solid where three or more sides intersect or where two sides intersect in a plane figure. Therefore, a vertex is a corner in a rectangle. There is another definition of a vertex, which is defined as a point farthest from the base.