Tetrahedron
Pronunciation: /ˌtɛ trəˈhi drən/ Explain
 Figure 1: Regular tetrahedron. Image courtesy Wikipedia.org. 
 Manipulative 1  Irregular tetrahedron. Created with GeoGebra. 

A tetrahedron is any foursided
polyhedron
(see figure 1). The sides of a regular tetrahedron are
equilateral triangles.
Manipulative 1 shows one form of an irregular tetrahedron. Click on the blue points
and drag them to change the figure.
Discovery: Click on the blue points in manipulative 1 and drag them. Try
to create a
concave
tetrahedron. Is it possible to make a concave tetrahedron? Why or why not?
Formula for Regular Tetrahedron
a is the length of an edge. 
Name  Formula 
Base plane area  
Surface Area  
Height  
Volume  
Table 1 

Nets for Tetrahedron
A geometric net is a 2dimensional drawing containing polygons that can be
folded into a 3dimensional polyhedron. Figure 2 shows a net for a regular
tetrahedron. Click to get a
net of a regular tetrahedron
you can print, cut out and fold into a tetrahedron.

Figure 2: Net of a regular tetrahedron 
An irregular tetrahedron can be formed out of four triangles. Each of the triangles must
have one edge the same length as each of the other three triangles. Figure 3 contains
a net for an irregular tetrahedron that you can change. Click on the blue points and drag
them to change the figure. To print the net, print the entire page. For best results,
make your net as large as the box.

Manipulative 2: Net for an irregular tetrahedron. Created with GeoGebra. 
Truncated Tetrahedron
 Figure 3: Truncated tetrahedron. Image courtesy wikipedia.org. 

A truncated tetrahedron is a tetrahedron with the vertices
cut off. Figure 3 shows a regular truncated tetrahedron. Click to get a
printable net of a truncated tetrahedron.

References
 Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pp 4849. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 12/31/2009. http://www.archive.org/stream/elementsofconstr00noetrich#page/48/mode/1up. Buy the book
More Information
 McAdams, David E. Polyhedron. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/p/polyhedron.html.
Cite this article as:
McAdams, David E. Tetrahedron. 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/t/tetrahedron.html.
Image Credits
Revision History
12/31/2009: Added "References". (
McAdams, David E.)
9/25/2008: Initial version. (
McAdams, David E.)