How is a Cube a Convex Polyhedron, whereas a Star Polyhedron a Concave Polyhedron with respect to the AB line segment drawn in both the cases? The figures explained above are confusing. What if the line segment AB moved inside the Star Polyhedron, would it be a Convex Polyhedron then?
How is a Cube a Convex Polyhedron, whereas a Star Polyhedron a Concave Polyhedron with respect to the AB line segment drawn in both the cases? The figures explained above are confusing. What if the line segment AB moved inside the Star Polyhedron, would it be a Convex Polyhedron then?
A polygon is said to be convex, if the line segment joining any two points of the polyhedron is contained in the interior or on the surface if the polyhedron whereas a polygon is said to be concave, if the line segment joining any two points of the polygon is not contained in the interior or on the surface of the polyhedron.
For the cube, the line joining any two points A and B is always contained either in the cube or on the surface of the cube. Hence, a cube is convex polyhedron.
For the star shaped polyhedron, the line joining any two points A and B is not always contained either in the polyhedron or on the surface of the polyhedron. Hence, the star shaped polyhedron is a concave polygon.
A polygon is said to be convex, if the line segment joining any two points of the polyhedron is contained in the interior or on the surface if the polyhedron whereas a polygon is said to be concave, if the line segment joining any two points of the polygon is not contained in the interior or on the surface of the polyhedron.
For the cube, the line joining any two points A and B is always contained either in the cube or on the surface of the cube. Hence, a cube is convex polyhedron.
For the star shaped polyhedron, the line joining any two points A and B is not always contained either in the polyhedron or on the surface of the polyhedron. Hence, the star shaped polyhedron is a concave polygon.
