# Polyhedron. What is it? A polyhedron is a solid bounded by flat polygons, which are called faces.

Examples of polyhedra: The sides of the faces are called edges, and their corners are called vertices. Depending on the number of faces one can specify a tetrahedron (4 faces), pentahedron (5 faces), etc. A polyhedron is considered to be convex if it is located on one side of the plane of each of its faces. A polyhedron is called regular if its faces are regular polygons (i.e., where all sides and angles are equal) and all polyhedral angles at the vertices are equal. There are five types of regular polyhedra: tetrahedron, cube (regular hexahedron), octahedron, dodecahedron, icosahedron.

In a three-dimensional space a polyhedron (the concept of a polyhedron) is a set of finite number of flat polygons where

1) Every side of a polygon is a side of the other one (but only one), called adjacent to the first one (along this side);

2) Every polygon, which is a part of a polyhedron, can be reached by using another polygon adjacent to it, and this one in turn can be used to reach another adjacent polygon, etc.

These polygons are called faces, their sides are called edges, and their vertices are the vertices of the polyhedron. polyhedron vertices polyhedron edges polyhedron faces

A polyhedron is said to be convex if it is located on one side of the plane of each of its faces.

This definition implies that all faces of a convex polyhedron are flat convex polygons. The surface of a convex polyhedron consists of faces that lie on different planes. At the same time, the sides of polygons are the edges of polyhedron, the vertices of the polyhedron are the vertices of its faces, and the plane angles of the polyhedron are the angles of its polygons-faces.

A convex polyhedron is called a prismatoid if its vertices lie in two parallel planes. Prisms, pyramids and truncated pyramids are particular cases of a prismatoid. All lateral faces of a prismatoid are triangles or quadrangles, while quadrangular faces are trapezoids or parallelograms.

### Popular

The most durable construction

Which geometric solid known to us has the greatest strength? Which is most resistant to external...

Truncated great dodecahedron from metal

The monument to the “Truncated large dodecahedron” polyhedron was discovered in Obninsk (Russia)...

Polyhedron as an emblem of the town

The founders of the city of Mirny, located in the Arkhangelsk region, placed a polyhedron, the...

Polyhedra - Interior Items

Polyhedra can be an ornament to your home, creating a zest in the...

Children's playground

Summer is the time you want to spend outdoors. At the desk, the children will sit down in...

Outer sphere of polyhedra

The perfection of the spherical shape has long attracted the attention of thinkers and scientists...

Polyhedra in architecture. Part 2

The “business card” of the Republic of Belarus is a new building of the National Library in Minsk....