# Polyhedron

Pronunciation: /ˌpɒ.liˈhi.drən/ Explain
plural - polyhedra

Polyhedra
Number
of Sides
NameExample
4tetrahedron
5pentahedron.html
6hexahedron
7heptahedron
8octahedron
9nonahedronnone
10decahedron
11undecahedronnone
12dodecahedron
20icosahedron
24icositetrahedron
30triacontahedron
32icosidodecahedron
60hexecontahedron
90enneacontahedron
Table 1: Polyhedra.

A polyhedron is a 3-dimensional shape with sides made of polygons. The simplest polyhedron is the tetrahedron, a four sided figure with each side a triangle. A regular tetrahedron has sides that are equilateral triangles. Polyhedra may be concave or convex. The word polyhedron is from the Greek poly (many) and the Indo-European hedron (seat or face).

 Click on the blue points and drag them to change the figure. Click on an empty spot on the screen and drag to rotate the figure. Manipulative 1 - Parts of a Polyhedron Created with GeoGebra.

Each polyhedron contains faces, edges, and vertices. A face of a polyhedron is a polygon, a flat, 2-dimensional shape that make up the boundary of the polyhedron. An edge is where 2 faces join. A vertex of a polyhedron is where two or more edges meet.

The Euler-Descarte polyhedron formula relates the number of faces, edges and vertices of convex polyhedra:
V + F - E = 2
In the Euler-Descartes formula, V is the number of vertices, F is the number of faces, and E is the number of edges.

Polyhedra are named for the number of sides they possess and, sometimes, the shape of the faces. However, there may be than one shape that qualifies for each name. Click on the name in the table to find out more about that class of polyhedra.

### References

1. McAdams, David E.. All Math Words Dictionary, polyhedron. 2nd Classroom edition 20150108-4799968. pg 142. Life is a Story Problem LLC. January 8, 2015. Buy the book

• Malkevitch, Joseph. Euler's Polyhedral Formula. ams.org. American Mathematical Society. 2/6/2010. http://www.ams.org/featurecolumn/archive/eulers-formula.html.

McAdams, David E. Polyhedron. 4/27/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/p/polyhedron.html.

### Revision History

4/27/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)