The multi-purpose hexagon, October 98

(A) The hexagonal board below is the base of 2 polyhedra which form a cube, once assembled. Can you draw the polyhedra model(s)?
(B) Are you able to cut the hexagon below into: a) 5 pieces and b) 9 symmetrical pieces, in order to form with them an equilateral triangle?

Hexagonal board
 hexagonal board
© 1996-1998, Sarcone & Waeber, Lausanne

Here is the first solution (A)
 solution 1

And here, the second ones (B)
 solution 2

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