/*
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
*/