Tetrahedron
Pronunciation: /ˌtɛ.trəˈhi.drən/ Explain
Click on the blue points and drag them to change the figure.
Try to create a
concave
tetrahedron. Is it possible to make a concave tetrahedron? Why or why not?
 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.
Formulas 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.
Click on the blue points and drag them to change the figure.
What happens if the lines cross? Can you still build the net?

Manipulative 2  Net of a Irregular Tetrahedron Created with GeoGebra. 
Truncated Tetrahedron
Click on the blue points and drag them to change the figure.
 Manipulative 3  Truncated Tetrahedron Created with GeoGebra. 

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 12/16/2018. 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. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/t/tetrahedron.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/13/2018: Removed broken links, updated license, implemented new markup. Changed geogebra to new format. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
12/31/2009: Added "References". (
McAdams, David E.)
9/25/2008: Initial version. (
McAdams, David E.)