Question

Identify the convex polyhedron.

A.

B.

C.

D.

Answer 1

Hint: First we understand what is a convex polyhedron, and what are its features, then we try and analyze each and every figure and we draw conclusions as to which satisfies all the properties, that figure will be our required answered.

Complete step by step answer:

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 of the surface.
As looking at the given diagrams,

In option A

If we draw a line from 2 points of the polyhedron we can see that the line segment is not contained in the interior of the surface. So, this is not a convex polyhedron.

In option C

If we draw a line from 2 points of the polyhedron we can see that the line segment is not contained in the interior of the surface. So, this is not a convex polyhedron.

In option D

If we draw a line from 2 points of the polyhedron we can see that the line segment is not contained in the interior of the surface. So, this is not a convex polyhedron.

Whereas for option (B) is satisfying the above condition as it’s surfaces are not intersecting itself and the line segment form by two points is contained to the interior of the surface.

Hence, option (B) is the correct answer.

Note: A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedron. A polyhedron is a 3-dimensional example of the more general polytope in any number of dimensions.
A concave polyhedron is a polyhedron with the property that there exist two points inside it such that the line segment drawn between them contains points, not in the polyhedron. In other words, a polyhedron is concave exactly when it is not convex.