[I posted this on math.stackexchange, but got no answers.][1]

It is easy to divide a 2-gon into 3 congruent line segments. It is also easy to divide a triangle into 4 smaller triangles that are congruent. One of Martin Gardner's favorite problems (as he writes in one of his books) is to show that one can divide a square (regular 4-gon) into five congruent and connected pieces.

**The natural question is then: can one subdivide a regular pentagon into six congruent connected pieces?**

This sounds related to [Monsky's theorem][2].


  [1]: https://math.stackexchange.com/questions/1986938/subdividing-regular-pentagon-into-six-congruent-pieces
  [2]: https://en.wikipedia.org/wiki/Monsky%27s_theorem