David Fontaine wrote:
> 
> Andrea Ryan wrote:
> >
> > I have made #declares of meshes for the tetrahedron, cube and
> > octahedron.  I saw some vertexes of the dodecahedron and the icosahedron
> > in another polyhedra include file.  They used the golden ratio.  Is
> > there a reason for this?  I want to have the edges have lengths of one.
> 
> Yes!  If you have an icosahedron with edge lengths of one, you can
> inscribe three mutually orthogonal golden rectangles.  With the
> dodecahedron, you can inscribe three mutually orthogonal rectangles in
> the ratio phi^2 (which incidentally is phi + 1).

Oh, of course, the edge length doesn't matter.  But the shorter sides of
the rectangles are opposite edges, so if the edge length is one, the
length of the other sides are just phi or phi^2.

-- 
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

Post a reply to this message