Polyhedron
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.
Types of Polyhedra
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.
Types of Polyhedra by the Number of Faces
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.
