Paper Models of Polyhedra

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What is a Polyhedron?
A polyhedron (plural: polyhedra) is a three - dimensional figure made up of sides called faces, each face being a polygon.
(Extensive definition at Mathworld)

Platonic Solids
There are five so named because they were known at the time of Plato circa (427-347 BC).  These polyhedra are also called regular polyhedra because they are made up of faces that are all the same regular polygon.
Pictures and more information

Archimedean Solids
Key characteristics of the Archimedean solids are that each face is a regular polygon, and around every vertex, the same polygons appear in the same sequence, for example, hexagon - hexagon – triangle in the truncated tetrahedron Two or more different polygons appear in each of the Archimedean solids, unlike the Platonic solids which each contain only one single type of polygon.
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Truncated Tetrahedron:



Polygon
A polygon is a two dimensional figure made up of line segments called edges, that are connected two at a time at their endpoints. In a polyhedron, several polygonal faces meet at a corner (vertex). When all the edges of the polygon are of equal length the polygon is called regular. Polygons whose sides and angles are not of equal measure, are said to be irregular.

A polygon is a closed plane figure bounded by straight line segments. The line segments are called the sides of the polygon, and the points at which they intersect are called vertices. A polygon has the same number of sides as it has vertices.

Regular Polygons
If all the sides and all the angles of a polygon are equal the polygon is said to be regular.

Examples regular polygons: Triangle, Square and Pentagon

Irregular Polygons
Irregular Polygons have sides of differing lengths and angles of differing measure.  Unless all the sides of the polygon are of the same length and all the angles are of the same measure the polygon is said to be irregular. 

Examples irregular polygons: Triangle, Tetragon and Pentagon

Convex and Concave Polygons
The polygons above are all convex.

A planar polygon is convex if it contains all the line segments connecting any pair of its points.

A concave polygon is a polygon that is not convex. A polygon is concave if at least one of its internal angles is greater than 180°.

Names of polygons
Polygons are classified according to the number of sides they have. A polygon with n sides is called an n-gon
Greek prefixes used in naming polygons and polyhedra:

• 1 mono
• 2 di
• 3 tri
• 4 tetra
• 5 penta
• 6 hexa
• 7 hepta
• 8 octa
• 9 ennea
• 10 deca
  More numbers

For names of polyhedra see this.

Pictures of the Polyhedra models