Taking two diagonals of two opposite sides of a cube and attaching them properly we get a tetrahedron.

The volume of the tetrahedron is one third of the cube that contains it.

If the tetrahedron edge length is 1 then the cube edge length w is:

Then, the volume of a tetrahedron with edge length 1 is:

And, the volume of a tetrahedron with edge length a is:

This construction can be generalized to any parallelepiped and we get not regular "tetrahedra" .

The volume of one of these tetrahedra is one third of the parallelepiped that contains it.

LINKS

	Sections on a tetrahedron Special sections of a tetrahedron are rectangles (and even squares)
	Sections in Howard Eves's tetrahedron Howard Eves, mathematician and historian of Mathematics, received the George Polya Award for the article Two Surprising Theorems on Cavalieri Congruence
	Sections in the sphere We want to study a surprising Cavalieri congruence between a sphere and a tetrahedron. In this page we can see sections in a sphere.
	Surprising Cavalieri congruence between a sphere and a tetrahedronn We show a sphere and the Howard Eves's tetrahedron with congruent sections.
	Volume of an octahedron The volume of an octahedron is four times the volume of a tetrahedron. It is easy to calculate and then we can get the volume of a tetrahedron.
	The volume of an stellated octahedron (stella octangula) The stellated octahedron was drawn by Leonardo for Luca Pacioli's book 'De Divina Proportione'. A hundred years later, Kepler named it stella octangula.
	The volume of a cuboctahedron A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of a cube.
	The volume of a cuboctahedron (II) A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of an octahedron.
	The volume of a truncated octahedron The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces and 6 square faces. Its volume can be calculated knowing the volume of an octahedron.
	The truncated octahedron is a space-filling polyhedron These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling.
	Leonardo da Vinci: Drawing of a truncated octahedron made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the truncated octahedron.
	Leonardo da Vinci: Drawing of a cuboctahedron made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the cuboctahedron.
	Leonardo da Vinci: Drawing of a dodecahedron made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the dodecahedron.
	Leonardo da Vinci:Drawing of an stellated octahedron (stella octangula) made to Luca Pacioli's De divina proportione. Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the stellated octahedron (stella octangula).