The volume of the octahedron
The experience of building an octahedron with paper or using 12 plastic tubes forming 4 squares in three orthogonal planes, or just piling 6 oranges is not replaced with a two dimensional representation.
An interactive application can remind us how can we take a look at a octahedron.
An octahedron is composed by two pyramids of square base. We can see the height of these two pyramides as the diagonal of a square.
Therefore, the volume of an octahedron is:
With one octahedron and four tetrahedra we get a big tetrahedron. The volume of this tetrahedron is 8 times the volumen of one of the small tetrahedra. We see that the volume of the octahedron is four times that of the tetrahedron. Then we can recalculte the volume of a tetrahedron.
A vertical control allow us to see the four tetrahedra.
Using the other control we get a figure that remind us some drawings by Leonardo da Vinci.
By clicking and dragging on the figure we can rotate it.
It is easy to build with plastic tubes a figure formed by four tetrahedra and a octahedron.
