3-5 Configuration

We usually use 30 units to make a kusudama because
icosahedron or dodecahedron has 30 edges, and
we use each unit as an edge of regular polyhedron.

Icosahedron by Michael Naylor
        _-_.
     _-',^. `-_.
 ._-' ,'   `.   `-_ 
!`-_._________`-':::
!   /\        /\::::
;  /  \      /..\:::
! /    \    /....\::
!/      \  /......\:
;--.___. \/_.__.--;; 
 '-_    `:!;;;;;;;'
    `-_, :!;;;''
        `-!'         

Dodecahedron by Michael Naylor
      _----------_,
    ,"__         _-:, 
   /    ""--_--""...:\
  /         |.........\
 /          |..........\
/,         _'_........./:
! -,    _-"   "-_... ,;;:
\   -_-"         "-_/;;;;
 \   \             /;;;;'
  \   \           /;;;;
   '.  \         /;;;'
     "-_\_______/;;'

The properties of icosahedron are:

• every face is a triangle;
• every vertex has 5 triangles around.

When we assemble a 30-unit kusudama,
we just count around 3 and 5
no need to think of where are we in the icosahedron.

Also the same as dodecahedron, its properties are:

• every face is a pentagon;
• every vertex has 3 pentagons around.

It is also 3-5 configuration,
so it is easy to remember how to assemble 30 units.