June 26, 2019

Chapters

A polyhedron is a three dimensional region of space bounded by polygons.

### Faces

The faces of a polyhedron are each of the two dimensional polygons that border the polyhedron.

### Edges

The edges of a polyhedron are the sides of the faces of the polyhedron. Two faces have an edge in common.

### Vertices

The vertices of a polyhedron are the vertices of each of the faces of the polyhedron. Three faces coincide with the same vertex.

### Dihedral Angles

The dihedral angles are formed between two faces of all neighboring polygons.

### Polyhedral Angles

Polyhedral angles are formed by three or more faces of the polyhedron and have a common vertex.

### Diagonals

The diagonals of a polyhedron are the line segments joining two vertices not belonging to the same face.

## Euler's formula

It is verified that in all convex polyhedra:

**No. of faces + No. of vertices = No. of de edges + 2.**

### Convex Polyhedron

In a convex polyhedron, a straight line can only penetrate the surface in two points.

### Concave Polyhedron

In a concave polyhedron, a straight line can pentrate the surface in more than two points.

### Regular Polyhedra

A regular polyhedron is composed of angles and faces (regular polygons) that are all equal.

## Platonic Solids

The platonic solids are convex regular polyhedra. There are exactly five types of platonic solids:

### Irregular Polyhedra

An irregular polyhedron is defined by polygons that are composed of elements that are not all equal.

## Tetrahedron

Polyhedron of 4 faces.

## Pentahedron

Polyhedron of 5 faces.

## Hexahedron

Polyhedron of 6 faces.

## Heptahedron

Polyhedron of 7 faces.

## Octahedron

Polyhedron of 8 faces.

## Nonahedron

Polyhedron of 9 faces.

## Decahedron

Polyhedron of 10 faces.

## Undecahedron

Polyhedron of 11 faces.

## Dodecahedron

Polyhedron of 12 faces.

## Icosahedron

Polyhedron of 20 faces.