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how to construct icosahedron or dodekahedron?

maybe for the first sight it seems to be very hard,
but math is very gracious in this case.

look at this scheme...

                    Y+
                    |
                    | ,
                    |/|    Z+
                    / |   /
                   /  |  /
                  |   |______
                  |   |     /
        +---------| ,------+----+
        |         | |           |
  X- ---|      ,--| +----,      |--- X+
        |     /   |/    /       |
        +----/    '    /--------+
            /_________/
                / |  /
               /  | /
              /   |/|
            Z-    ' |
                    |
                    Y-

do you see three rectangles in the 3d space with the united gravity center?
i hope you do.

so, let's look at one of those rectangles little bit closer.

 A          a          B  There is a secret rule in it.
 +---------------------+
 |                     |   a
 |                     |  --- = PHI
b|          +          |   b
 |                     |  
 |                     |  oh yea, that PHI. the Golden ratio (1.61803399...)
 +---------------------+
 C                     D

now, it is pretty easy to construct this rectagle, isn't it?

let's continue with an icosahedron, which vertices is contructed
with the scheme as you can see at thi first "picture".


                    Y+       rectagle positions in planes  
                    | B             rect | plane
                    | ,            ------+-------
                    |/|    Z+       ABCD |  YZ
                    / |   /         EFGH |  XY
                 A /  |  /          IJKL |  XZ
                  |   |______K
       E          |   |     /    F
        +---------| ,------+----+
        |         | |           |
  X- ---|      ,--| +----,      |--- X+
        |     /   |/    /       |
        +----/    '    /--------+
       G    /_________/ C        H
            I   / |  /L
               /  | /
              /   |/|
            Z-    ' |
                  D |
                    Y-

finnaly, incosahedron is construsted with this triangles

1. ABE    9. DLG   17. EGJ
2. AEI   10. DGI   18. EGI
3. AIL   11. DIL   19. FHC
4. ALF   12. DLH   20. FHK
5. BAF   13. LDH
6. BFK   14. LHK
7. BKJ   15. LKJ
8. BJE   16. LJG



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