Tetrahedron

Pronunciation: /ˌtɛ trəˈhi drən/ ?

Figure 1: Regular tetrahedron. Image courtesy Wikipedia.org.

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Manipulative 1 - Irregular tetrahedron.
Created with GeoGebra.

A tetrahedron is any four-sided 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.
NameFormula
Base plane areabase plane area = (3/16)*a^2
Surface Areasurface area=square root(3)*a^2
Heighth=square root(2/3)*a
VolumeV=square root(1/72)*a^3
Table 1

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.

Net of a tetrahedron which is three isosceles triangles with an edge in common with a forth.
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.

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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

  1. 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.
  2. 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=.

More Information

  • 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.

Translations

Image Credits

Revision History


2009-12-31: Added "References" (McAdams, David.)
2008-09-25: Initial version (McAdams, David.)

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