So as to answer this question, we need to start with the definition of each concept. The prism is a geometric solid and it is known as being a convex polyhedron having two congruent and parallel bases (equal polyhedrons). Depending on the number of sides of the polygon which forms the bases, we can have: triangular prism (its base is a triangle); quadrangular prism (its base i a quadrilateral); pentagonal prism (its base is a pentagon); hexagonal prism (its base is a hexagon) and so on.

A parallelepiped is the designation given to a prism whose faces are parallelograms. When we are referring to bases we also include the bases. It happens that the base of a quadrangular prism can be a kite. Having in mind that a kite is a quadrilateral, but not a parallelogram, we can conclude that not all the quadrangular prisms can be called parallelepipeds. But the contrary is true: all the parallelepipeds are necessarily quadrangular prisms!

And... what about the cube? Everybody knows that it is a polyhedron composed of 6 square faces (parallelograms). According to this definition we arrive to the conclusion that a cube is a quadrangular prism and so it is also a parallelepiped.

Check out our List of Questions to get to know a little more about the most diverse topics related to mathematics. If you have any pertinent (math) question whose answer can not easily be found, send us an email on the Contact page with the question. We will be happy to respond. In the event that you detect any errors in our answers, do not hesitate to contact us!