[list][*]Start from a regelar pentagon with center [math]O=\left(0,0,0\right)[/math] and radius [math]r=1[/math].[/*][*]Create a dodecahedron out of it.[/*][*]Out of the properties of a dodecahedron you can define the coordinates of the points V and W:[br]V is the center of gravity of a pentagon adjacent to the base of the dodecahedron.[br]W is the center of gravity of a pentagon, connected to the base by one pentagon.[/*][*]You can calculate |OV| en |OW| out of the coordinates of V and W.[/*][*]The proportion [math]\frac{\left|OW\right|}{\left|OV\right|}=\frac{1+\sqrt{5}}{2}=\Phi[/math][br][/*][*]The points O, V and W define a rectangle. [br]With edges [OW] en [OV] you get [math]\frac{l}{w}=\frac{1+\sqrt{5}}{2}=\Phi[/math].[/*][*]This rectangle connects 4 midmidpoints of faces of the dodecahedron.[br]In a dodecahedron you can create 3 such quartets, defining 3 rectangles, perpendicular to each other.[/*][/list]In other words: [b]"In a dodecahedron one can create 3 perpendicular golden ractangles"[/b] follows from the property:[br][b]"The proportion of the distance between the centers of gravity of a face and the center of gravity of a face connected to the first face by just one face and the distance between the centers of gravity of two adjacent faces equals [/b][math]\frac{1+\sqrt{5}}{2}[/math][b]."[/b]