Tetrahedron

Pronunciation: /ˌtɛ.trəˈhi.drən/ Explain

Tetrahedron with four faces that are equilateral triangles.

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 four-sided polyhedron (see figure 1). The sides of a regular tetrahedron are equilateral triangles.

Formulas 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.

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

  1. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pp 48-49. 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.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License