Home > 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.

Pictures and models of Archimedean solids

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

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