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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.
A polyhedron is said to be convex if its surface (comprising its faces, edges and vertices) does not intersect itself and the line segment joining any two points of the polyhedron is contained in the interior or surface. A polyhedron is a 3-dimensional example of the more general polytope in any number of dimensions.olyhedra with congruent regular faces of six or more sides are all non-convex, because the vertex of three regular hexagons defines a plane. The total number of convex polyhedra with equal regular faces is thus ten, comprising the five Platonic solids and the five non-uniform deltahedra.