This problem was inspired by Kadon's Puzzling Pentagon. A picture of this puzzle can be seen at this page
. It is made up of four pentagons, each dissected identically into four golden triangles. The triangles can be assembled into one large pentagon.
Suppose we take this puzzle and make a tray for the pieces. On the tray we want to draw a grid as a guide to place the pieces. The edges of the grid would represent all the legal edge positions of pieces for any valid solution. What should the grid look like?