What is a Tetrahedron?

Image Credit: 
Main Image: 

A tetrahedron is a 3 dimensional geometric figure. It is the smallest polyhedron. It is composed 4 triangular faces, 3 of which merges at each vertex. This figure is used extensively in architecture and modern art. Tetrahedron is also used for solving complicated geometric problems. Once we understand the structure then it will become very easy to detect a tetrahedron around us.


How does a Tetrahedron look like?

Firstly, we need to know more about other 2 dimensional geometric shapes to visualize a tetrahedron. Let us find out about a polygon. A polygon is a 2 dimensional figure bounded by straight lines on all side. Examples of a polygon include triangle, square, rectangle and many more. The triangle is the smallest polygon. A polyhedron on the other hand is a 3 dimensional geometric figure. The most common type of polyhedron is the cube with 6 sides. The sides cannot be curved. In a tetrahedron the sides of the figure are made of triangles. Each side of the triangle is connected to other side. In this way they form a 3 dimensional figure. If all equal sided triangles are employed then a regular tetrahedron is formed. A tetrahedron looks like a triangular pyramid with a flat base and a tapering tip. 


How to build a Tetrahedron?

There are many interesting ways in which we can make a tetrahedron. With similar sized spheres we can make a tetrahedron. We can make layers to build a tetrahedron. Longer the tetrahedron, more number of layers of sphere will be required. In the first layer only one sphere will be required, in the next layer 3 and the next is 6. If “n” denotes the nth layer then number of spheres in any layer is given by the formula n(n+1)/2. If we add all these numbers in each layer then we will get the tetrahedral numbers which are 1,4, 10, 20 and so on. The summation is given by the formula n(n+1)(n+2)/6. There is another interesting way of forming a regular tetrahedron. If we draw the 4 space diagonals of a cube, it gets divided into six equal pyramids or tetrahedrons.


What is the most important property of a Tetrahedron?

A tetrahedron is a convex polyhedron. In a convex polyhedron we can choose any two random points on its surface and join with a line. This line passes through the body of the polyhedron. This property is satisfied by a tetrahedron. Moreover, the line joining two points of the tetrahedron can extend beyond the shape.  However, with increase in number of sides, this unique property of convex polyhedron gets violated. 


What are the applications of a Tetrahedron?  

Tetrahedron finds use in architecture, chemistry, geology, engineering, electronic fields, and contemporary art.

  • Architecture: Tetrahedron adds visual effects to designs, so this figure is found to be used by architects. They can specifically rotate a tetrahedron in the AutoCAD software to view all its surfaces and incorporate necessary changes. It is very easy to make other complex designs using tetrahedron
  • Electrical: It finds use in making electrical circuits and semiconductors used in (solid-state electronics). Tetrahedron shaped circuits can be used to reduce overall resistance in an electrical path.
  • Geology: Tetrahedral hypothesis published by William Lowthian Green explains the formation of the Earth.
  • Mathematics: Tetrahedron is used for explaining complicated finite element analysis used for partial differential equations. These methods are widely used in aerodynamics, electromagnetic fields, computational fluid dynamics, chemical engineering, civil engineering and naval architecture and engineering.
External References
Related Videos: 
See video
Related Images: