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.

Quite often a question about a practical use of paper models pops up. What is the point of paper...

The festival of fascinating science was held in Moscow on April 24 and 25, 2015 at the physics...

The most famous building in Kazan (city in Russia) and its main symbol is Tower Syuyumbike. It is...

Stamps cover all significant events happening in the world. Much attention was paid to polyhedra by...

Is it possible to conduct additional school classes in geometry collecting models of polyhedra? Of...

Is it possible to cut a triangle into such a number of parts so that one can put a square together?

What do you think the dodecahedron and the calendar have in...