We take for example the shape below that can be made with 15 soft diamonds :

Replace all circular arcs with segments :

We get the rectified shape of the initial shape ; if we take as initial shape a soft diamond, its rectified shape is still the traditional diamond ; examples :

2) Conjugated shapes :

Let’s get back to the starting shape :

This time, let’s replace all hollow circular arcs with bumpy circular arcs and vice versa :

We get the conjugated shape of the initial shape ; if we take as initial shape a soft diamond, there are 3 cases :

• if the initial soft diamond is in the series L1 to L10, its conjugate will be in the series L11 to L20.

• if the initial soft diamond is in the series L11 to L20, its conjugate will be in the series L1 to L10.

• if the initial soft diamond is in the series L21 to L27, it is its own conjugate.

Examples :

If we have a solution for a shape, the conjugated shape has at least one solution, obtained by replacing each soft diamond in the solution with its conjugated soft diamond.

♥ For example, here is a solution of the starting shape :

By passing to the conjugated soft diamonds, we obtain :

However, I couldn’t find a solution for the same shape rectified.

♥ Another example :

I have found a solution for the shape above.

I figured out a solution for the conjugated shape :

On the other hand, to my great regret, their rectified shape (above) has no solution !

3) Conjugated rectified shapes :

A rectfied shape has no circular arcs so, if we look for its conjugated shape, it will be the same as the initial shape.

Example :

If we have a solution for this shape, then we will have a second solution, obtained by replacing each soft diamond in the solution with its conjugated soft diamond.

Example :

On the same principle, you can search the conjugated solution of the solution for the hexagon of side 3 on the tray.