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Polyhedra are three-dimensional shapes made up of flat faces, with each face being a polygon. They can be named according to the number of faces they have and can be either convex or non-convex. They are used in various industries and are important in understanding mathematical concepts.
A polyhedron is a three-dimensional shape bounded by a series of flat planes known as faces. A simple example is a cube, a six-sided polyhedron made up of square faces. There is actually some dispute in the mathematical world as to what exactly constitutes a polyhedron, and some mathematical disciplines use the term to describe a very specific type of shape. For the most part, however, the definition of a three-dimensional shape characterized by having flat faces is reasonably accurate.
Each face of a polyhedron is a polygon, another type of geometric figure. Polygons are flat figures made with a series of connecting line segments that form a closed shape. A rectangle is a simple polygon created with four line segments, with a star being a more complex example of a polygon. The polygons in a polyhedron can vary considerably in size, shape, and arrangement, and when all polygons are identical, the resulting shape is known as a “symmetric polyhedron.”
As a general rule, a polyhedron is named according to the number of faces it has. An octahedron has eight faces, a dodecahedron has 12, and so on. Sometimes descriptive terms about the shape are also added. A pyramid, for example, is a special kind of four- or five-sided polyhedron. Stellated polyhedra have numerous pyramidal outcrops called stellations that create a series of points, giving the polyhedron a three-dimensional star shape.
Polyhedra can be either convex, meaning that a line drawn between any two points on the shape will pass through the shape without deviating beyond its boundaries, or non-convex, where the line passes outside the shape. A rectangular block is an example of a convex polyhedron: if you draw an imaginary line between any two points on the block, it will pass through the block. Conversely, a stellated polyhedron is non-convex, because the points that exit the shape’s body can be drawn between the stellations.
People interact with polyhedra every day, and their study is vital to a wide variety of industries. For example, many products are packaged in multifaceted containers, designed for optimal production efficiency and stackability. Many homes are of this shape, created with a series of floors that have been used to create an enclosed space. The study of polyhedra tends to be introduced to children at a young age, as understanding them can be key to understanding other mathematical concepts.
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