Polyhedrons are three dimensional shapes in geometry that can have any number of faces as long as it forms a solid enclosed space. Polyhedra can have any number of bases but the most common have either 1-pyramid or 2-prism. Additionally all of the edges must be straight. As a result spheres and cylinders are not considered polyhedra. The names of polyhedra can range from the unusual like dodecahedron to the more familiar such as the cube. Faces, bases, edges, and vertices define the shape and size of the polyhedron by their relative measurements.
A pyramid is a recognizable shape and is considered a polyhedron. Pyramids need to be identified by the base. The base in the case of a pyramid would be the side that is touching the ground. If you look at a pyramid from an aerial view you would easily see the shape of the base. It could be a triangle, rectangle, or any other polygon shape. Remember a polygon is a two dimensional shape that can have any number of sides. If a pyramid’s base has 4 edges then the pyramid itself will have 4 sides. These sides of the pyramid are called faces and the have to be triangles in order for the shape to be a pyramid.
The prism is the polyhedron that has rectangular sides. The prism also differs from the pyramid because it has 2 bases. These bases are defined as being congruent and all of the lateral faces must be parallel. Congruent in geometry means they have the same size and shape. If the base of the prism is a pentagon then the prism will have 2 bases that are pentagons and 5 lateral faces because pentagon is a 5 sided polygon.
Regluar polyhdra are polyhedrons that have congruent faces equidistant from the center of the 3D object, and have the same arrangement at each vertex. The faces must be regular polygons which means each polygon has sides measuring the same length. The regular pyramid can be considered a triangular pyramid since the base is a triangle but what makes it regular is that all of the faces including the base are congruent. This solid is also known as a tetrahedron. The next would be the cube which is made up of square faces. There are 5 total convex regular polyhedrons including the dodecahedron and icosahedron.
Polyhedrons are used in construction and mathematical formulas have been derived to show relationships do exist to determine the volume and surface areas of polyhedrons given limited information. This can be useful to manufactures that need to calculate how much material is needed to make a new product.