What is a Polyhedron?
A polyhedron is a three dimensional shape bounded by a series of flat planes which are known as faces. A simple example of a polyhedron is a cube, a six-faced polyhedron made with square faces. There is actually some dispute in the math world about what constitutes a polyhedron, exactly, and some mathematical disciplines use the term “polyhedron” 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 which 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 in size, shape, and arrangement considerably, and when all of the polygons are identical, the resulting polyhedron is known as a “symmetrical pol
We can at least say that a polyhedron is built up from different kinds of element or entity, each associated with a different number of dimensions: • 3 dimensions: The body is bounded by the faces, and is usually the volume inside them. • 2 dimensions: A face is bounded by a circuit of edges, and is usually a flat (plane) region called a polygon. The faces together make up the polyhedral surface. • 1 dimension: An edge joins one vertex to another and one face to another, and is usually a line of some kind. The edges together make up the polyhedral skeleton. • 0 dimensions: A vertex (plural vertices) is a corner point. • -1 dimension: The nullity is a kind of non-entity required by abstract theories. Most of us need not worry about it. More generally in mathematics and other disciplines, “polyhedron” is used to refer to a variety of related constructs, some geometric and others purely algebraic or abstract. A polyhedron is a 3-dimensional example of the more general polytope in any numb
A polyhedron (plural: polyhedra) is a three – dimensional figure made up of sides called faces, each face being a polygon. (Extensive definition at Mathworld) Platonic Solids There are five so named because they were known at the time of Plato circa (427-347 BC). These polyhedra are also called regular polyhedra because they are made up of faces that are all the same regular polygon. Pictures and more information Archimedean Solids Key characteristics of the Archimedean solids are that each face is a regular polygon, and around every vertex, the same polygons appear in the same sequence, for example, hexagon – hexagon triangle in the truncated tetrahedron Two or more different polygons appear in each of the Archimedean solids, unlike the Platonic solids which each contain only one single type of polygon. Pictures and more information Truncated Tetrahedron: Polygon A polygon is a two dimensional figure made up of line segments called edges, that are connected two at a time at their endp
A polyhedron is a three-dimensional solid whose faces are polygons joined at their edges. A polyhedron is said to be regular if its faces are made up of regular polygons. A regular polygon is a polygon with sides of equal length placed symmetrically around a common center. The word polyhedron is derived from the Greek poly (many) and the Indo-European hedron (seat).
