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.
The diagonal of a square of edge length 1 is:
Therefore, the volume of an octahedron of edge length 1 is:
And the volume of an octahedron of edge length a is:
Using that we can calculate the volume of a tetrahedron. We can consider a tetrahedron of edge length 2:
We can write a relation:
A tetrahedron of edge length 2 is made of one octahedron and four tetrahedra of edge length 1:
Then, the volume of an octahedron is four times the volume of a tetrahedron and we can recalculate the volume of a tetrahedron.
It is easy to build with plastic tubes a figure formed by four tetrahedra and one octahedron.