Prism (geometry)

Imagine you have two identical flat shapes. If you stack them perfectly on top of each other, you create a solid object. This object is called a prism.

A prism is a type of polyhedron, which is a solid with flat faces. It always has two bases that are the same size and shape. These bases are connected by other faces that are all parallelograms. If you slice through a prism anywhere parallel to the bases, the new shape is exactly like the bases. We name these shapes based on their ends. A prism with a five-sided base is a pentagonal prism.

Prisms can stand straight or lean to the side. A right prism stands perfectly upright. Its side faces are rectangles because they meet the bases at a right angle.

A right rectangular prism is often called a cuboid or a simple box. If the bases are squares, we call it a square prism. An oblique prism is different because it leans. In an oblique prism, the side edges are not perpendicular to the bases.

One special oblique prism is called a parallelepiped. This shape has six faces that are all parallelograms.

People have studied these shapes for a very long time. The word prism first appeared in a famous work called "Elements." This work was written by a mathematician named Euclid.

In Book XI of his work, Euclid defined a prism. He described it as a solid figure held by two equal and parallel planes. The other sides must be parallelograms. Some later writers found his definition a bit confusing. They felt it did not explain the bases clearly enough. This caused some debate among geometry students for many years.

There are many ways to change or twist a prism. You can make a star prism using star shapes for bases.

You can also make a twisted prism. This happens when you twist the top base. The simplest twisted prism is called a Schönhardt polyhedron.

If you slice a prism at an angle, you get a truncated prism. A frustum is another shape that looks similar but has different sized bases.

You can even make a crossed prism. This looks like an hourglass because the sides cross each other.

Math lets us see how these shapes grow and change. If you keep adding more sides to a prism's base, it changes. As the number of sides grows toward infinity, the prism looks like a cylinder.

We can also think about prisms in higher dimensions. These are called prismatic polytopes. A 4-dimensional prism is made by moving a 3-dimensional shape into a new direction. For example, a 4-4 duoprism exists in four-dimensional space.

This shows how math can describe shapes we cannot even see.