Question

Is it possible to have a polyhedron with any given number of faces? ( Hint: Think of a pyramid).

Answer 1

Hint: We will first visualize a pyramid as it is a polyhedron, and see how many faces it has, and then we will define what is a polyhedron and accordingly we will conclude our required answer, as to what is the minimum number of faces a figure should have to be a polyhedron.

Complete step-by-step answer:

Above is an image of a pyramid, we can clearly see it has 6 faces, hence it is a polyhedron.
It is possible to have a polyhedron with any given number of faces if the number of faces is greater than or equal to 4. A polyhedron must have at least a minimum of 4 faces. As it is a 3 dimensional figure with all the sides as polygons.
So, we come to a conclusion that it is not possible to have a polyhedron with any given number of faces.
The number of faces must be greater than or equal to 4.

Note: Polyhedron: A three-dimensional figure whose faces are all polygons.
Regular polyhedrons: A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.
Prism: A polyhedron whose bottom and top faces (known as bases) are congruent polygons & faces known as lateral faces are parallelograms.
When the side faces are rectangles, the shape is known as the right prism.
Pyramid: A polyhedron whose base is a polygon and lateral faces are triangles
with a common vertex.

A prism or a pyramid is named after its base. Thus a hexagonal prism has a hexagon as its base; and a triangular pyramid has a triangle as its base
Face: A flat surface of a three dimensional figure.
Edge: Line segment where two faces of solid meet
Vertex: A point where three or more edges meet.
Base: The face that is used to name a polyhedron.