Points of coordinates:

are the 20 vertices of a regular dodecahedron of edge 2.

Where Phi is the golden ratio we've seen in the golden rectangle.

We can calculate the distance between pairs of adjacents vertices to convince ourselves.

This is an interesting step in understanding properties of this polyhedron, for example, the volume of a regular dodecahedron.

One eighth of a dodecahedron of side 2 has the same volume as a dodecahedron of side 1.

LINKS

	Volume of a regular dodecahedron (Flash version) One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.
	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.
	The golden ratio From Euclid's definition of the division of a segment into its extreme and mean ratio we introduce a property of golden rectangles and we deduce the equation and the value of the golden ratio.
	The golden rectangle A golden rectangle is made of an square and another golden rectangle.
	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 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 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).
	The icosahedron and its volume The twelve vertices of an icosahedron lie in three golden rectangles. Then we can calculate the volume of an icosahedron
	The volume of the tetrahedron The volume of a tetrahedron is one third of the prism that contains it.
	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 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.