Polyhedron
Pronunciation: /ˌpɒ liˈhi drən/ Explain
plural  polyhedra
Polyhedra
Number of Sides  Name  Example 
4  tetrahedron  
5  pentahedron.html  
6  hexahedron  
7  heptahedron  
8  octahedron  
9  nonahedron  none 
10  decahedron  
11  undecahedron  none 
12  dodecahedron  
14  tetradecahedron  
20  icosahedron  
24  icositetrahedron  
30  triacontahedron  
32  icosidodecahedron  
60  hexecontahedron  
90  enneacontahedron  
Table 1: Polyhedra. 
A polyhedron is a 3dimensional 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
IndoEuropean 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,
2dimensional 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
EulerDescarte polyhedron
formula relates the number of faces,
edges and vertices of convex polyhedra:
In the EulerDescartes 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.
More Information
 Malkevitch, Joseph. Euler's Polyhedral Formula. ams.org. American Mathematical Society. 2/6/2010. http://www.ams.org/featurecolumn/archive/eulersformula.html.
Cite this article as:
McAdams, David E. Polyhedron. 12/4/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/polyhedron.html.
Image Credits
 All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons AttributionShareAlike 4.0 International License.
 Pentagonal prism: R. A. Nonenmacher, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 4.0 International, 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license. https://en.wikipedia.org/wiki/File:Pentagonal_Prism.svg.
 Square Dipyramid: Kjell André, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Octahedron.gif.
 Pentagonal Dipyramid: Capaccio, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license. https://en.wikipedia.org/wiki/File:Pentagonal_bipyramid.png.
 Regular Dodecahedron: Kjell André, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Dodecahedron.gif.
 Cuboctahedron: Cyp, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Cuboctahedron.gif.
 Regular icosahedron: Kjell André, https://commons.wikimedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://commons.wikimedia.org/wiki/File:Icosahedron.gif.
 Pentagonal icositetrahedron: Jim2k, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Pentagonalicositetrahedronccw.gif.
 Rhombic triacontahedron: Jim2k, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Rhombictriacontahedron.gif.
 Icosidodecahedron: Cyp, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Icosidodecahedron.gif.
 Pentagonal hexecontahedron: Jim2k, https://en.wikipedia.org. This file is licensed under the Creative Commons AttributionShare Alike 3.0 Unported license. https://en.wikipedia.org/wiki/File:Pentagonalhexecontahedronccw.gif.
 Rhombic Enneacontahedron: Tom Ruen, https://en.wikipedia.org. This work has been released into the public domain by its author, Tomruen at English Wikipedia. https://en.wikipedia.org/wiki/File:Rhombic_enneacontahedron.png.
Revision History
12/1/2018: Removed broken links, updated license, implemented new markup, updated geogebra app. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
1/6/2009: Added parts of a polyhedron, and the EulerDescarte polyhedron formula. (
McAdams, David E.)
9/25/2008: Initial version. (
McAdams, David E.)