When discussing shapes, it is important to understand the difference between a vertex and an apex. A vertex is a point at which two or more lines meet, while an apex is the highest point of a shape. It is possible for a shape to have a vertex that is also an apex, and this article will discuss which shapes have this property.

## Sphere

A sphere is a three-dimensional figure with no faces, edges, or vertices. The apex of a sphere is the same point as its center, making it the only shape in which the vertex and apex are the same.

## Prism

A prism is a three-dimensional figure with two congruent faces, called bases, and four lateral faces that are rectangular. The apex of a prism is the same point as the vertex of its base, making the vertex of the base both a vertex and an apex.

## Cylinder

A cylinder is a three-dimensional figure with two congruent circular faces and a curved lateral face. The apex of a cylinder is the same point as the vertex of its circular faces, making the vertex of the circular faces both a vertex and an apex.

## Pyramid

A pyramid is a three-dimensional figure with a polygonal base and triangular lateral faces. The apex of a pyramid is the same point as the vertex of its base, making the vertex of the base both a vertex and an apex.

In conclusion, it is possible for a shape to have a vertex that is also an apex. The shapes that have this property are the sphere, prism, cylinder, and pyramid.

Since ancient times, shapes have formed the basis of our understanding of the world around us. From 3D models to 2D drawings, the four basic shapes – sphere, prism, cylinder and pyramid – are common in both mathematics and the everyday physical world. But what happens when the vertex of a shape is also an apex? In this article, we’ll explore which shapes have a vertex that is also an apex – and what the implications of this are.

A sphere is a three-dimensional shape consisting of the points equidistant from the center of a circle. While the vertex of a sphere is not an apex, the shape itself does have an apex. This apex can be seen when a sphere is cut along a diameter – the two halves of the sphere will form a point at the top, which is the apex.

A prism is a three-dimensional figure with two parallel and identical ends. It has two faces that are parallel and the same shape. A prism’s vertex is the point where the two faces intersect, and it is also the apex of the shape.

A cylinder is a three-dimensional shape with two parallel and identical ends. The ends of the cylinder are two circles which are the same size and shape, and the vertex of the shape is the point where these circles intersect. This vertex is also the apex of the cylinder.

Finally, a pyramid is a three-dimensional shape with a polygonal base and a point at the top – this point is the apex of the shape. The vertex of a pyramid can also be its apex, depending on the number of sides of the polygon. For example, if a pyramid has four sides, then the vertex of the shape is also the apex.

So, in conclusion, among the four basic shapes – sphere, prism, cylinder and pyramid – only the pyramid has a vertex that can be an apex. This is due to the fact that the shape has a polygonal base and the vertex is at the intersection of the sides of the polygon. While the advent of 3D modelling and printing has made it possible to create more complex shapes than ever before, the classic four shapes remain at the foundation of our understanding of geometry and the world around us.