Polyhedra (Meaning and Explanation)

We explain what polyhedra are in geometry, their elements, classification and examples. Also, what are they called?

What are polyhedra?

According to classical geometry, certain polyhedra are called polyhedrons. three-dimensional geometric bodies, with flat faces and that contain a finite volume. That is to say, a polyhedron is a bounded portion of geometric space, limited by different polygons. Its name comes from the Greek word polyhedroncomposed of polys: “many”, and edra: “base” or “face.”

Its name depends on the number of faces it has using numeral prefixes of Greek descent and the ending –ahedron. For example: tetrahedra (4 faces), pentahedrons (5 faces), hexahedrons (6 faces) and so on. In addition, many polyhedra have their own names, such as cube, prism, pyramid, etc.

Elements of polyhedra

polycahedron elements — All polyhedra have the same elements, although in different quantities and shapes.

Polyhedra are made up of the following elements:

Faces The flat surfaces that delimit the internal space of the polyhedron. They are two-dimensional and are closed figures made up of lines. It can also be said that they are the polygons that constitute it. Among them the bases are usually distinguished, which are simply the faces on which the polyhedron rests.
Edges The lines that make up the body of a polyhedron, and at whose intersections the vertices appear.
Vertices The meeting angles between three or more edges in the body of a polyhedron.

Classification of polyhedra

Beyond giving them names according to their number of faces, as we explained at the beginning, polyhedra can be classified according to the shape and relationship of their faces, thus having:

regular polyhedra. When all its faces are regular polygons.
uniform polyhedra. When all their faces are equal to each other.
Irregular polyhedra. When they have faces that are unequal to each other.

Examples of polyhedra

dodecahedron polyhedra — A dodecahedron has twelve regular, uniform faces.

The following are examples of polyhedra:

Pyramids. Consisting of a base and various triangular faces.
Cubes. Made up of the union of six regular rectangles.
Parallelepipeds. Constructed by two regular squares and four rectangles equal to each other.
Prisms. Whose faces are parallelograms, as many as the sides have their two bases.
Dodecahedra. Concave or convex polyhedra with twelve regular and uniform faces.
Octahedron. Built by joining two pyramids at the base.

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