Pronunciation: /ˌtɛ trəˈhi drən/ ?
|Figure 1: Regular tetrahedron. Image courtesy Wikipedia.org.|
|Manipulative 1 - Irregular tetrahedron.|
Created with GeoGebra.
A tetrahedron is any four-sided
(see figure 1). The sides of a regular tetrahedron are
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
tetrahedron. Is it possible to make a concave tetrahedron? Why or why not?
Formula for Regular Tetrahedron
|a is the length of an edge.|
|Base plane area|
Nets for Tetrahedron
A geometric net is a 2-dimensional drawing containing polygons that can be
folded into a 3-dimensional 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.|
|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.
- Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented, pp 48-49. Translated by Noetling, William A.M, C.E.. Silver, Burdett & Company, 1897. (Accessed: 2009-12-31). http://www.archive.org/stream/elementsofconstr00noetrich#page/48/mode/1up.
- tetrahedron. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=tetrahedron&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
- McAdams, David. Polyhedron. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Polyhedron.
- McAdams, David. Geometric Net of a Regular Tetrahedron. LifeIsAStoryProblem.org. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.org/explore/net_tetrahedron.pdf.
- McAdams, David. Geometric Net of a Truncated Tetrahedron. LifeIsAStoryProblem.org. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.org/explore/net_truncated_tetrahedron.pdf.
Cite this article as:
Tetrahedron. 2008-09-25. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/t/tetrahedron.html.
2009-12-31: Added "References" (McAdams, David.
2008-09-25: Initial version (McAdams, David.