vertices of a pyramid

A vertex of a polyhedron is the point of intersection of three or more faces of the structure.

A pyramid is a polyhedron with a polygonal base connected to a single point called the apex.

The number of vertices of a pyramid varies with the different types of pyramids.


How to determine the number of vertices

In a pyramid, the side faces (originating from the apex) meet at the base.

pyramid

So basically, for the square pyramid shown above, the four vertices of the square base become four vertices of the pyramid.

In addition, we have the apex, where the slant surfaces meet.

Hence, in a pyramid with a n-sided polygon as base, we have (n+1) vertices.

Some examples of vertices of a pyramid.

Now let us try to find the number of vertices of some common pyramids.

triangular pyramid

This is a triangular pyramid, i.e., the base is a triangle (3-sided polygon).

Hence, the number of vertices would be (3+1) = 4


rectangular pyramid

This is a rectangular pyramid, i.e., the base is a rectangle (4-sided polygon).

Hence, the number of vertices would be (4+1) = 5


pentagonal pyramid

This is a pentagonal pyramid, i.e., the base is a pentagon (5-sided polygon).

Hence, the number of vertices would be (5+1) = 6


Thus, it is quite simple to find the number of vertices of a pyramid given we know the type of polygon it has as its base. The square pyramid (with a square as its base) is the most common type of pyramid found in various monuments all over the world.