How inscribe a regular hexagon in an irregular hexagon socket ?

Hello !

Following this question, I have make my geodesic sphere :
(I followed a tutorial, and this sphere is obtained by subdivise an icosahedron)

(The left view is orthogonal).

Now I want inscribe my (regular) hexagon mesh in the different (irregular) hexagon socket, like this :
(I make these screens with a manual modification, in Unity scene view)

(The views are orthogonal).

Currently, the only thing I'm doing correctly is the Y orientation (-y lookat the center of the sphere).

What I'm missing, to marry my hexagon to his socket is :

- The X rotation. (Taking into account the -y lookat)
- The X = Y = Z scale (I don't want deform him).
- The little X and Z offset position after having done the scale. (Currently is the center of gravity of the socket, but after do the scale, I need to slightly reposition the hexagon).

I don't know overly, how to take the problem and obtain what I want ...

The variables I have :
- The transform of my hexagon mesh (and all GameObject properties ... MeshRenderer, MeshFilter ...)
- The positions (Vector3) of the socket

Can you help me ???
Thanks !

 

I found a solution, for the scale, but the rotation still a problem ...
I have test many solution, but none is perfect.

Here my actual result. You can see a offset for the hexagons near of the pentagons.

In this standalone, for the scale, I use a formule involving the perimeter of the socket, and a lambda multiplicator.
For the rotation, my X (red arrow of the pivot) look an angle of the socket (the closest when the hexagon mesh is instantiate to the position). But for some hexagons socket, is not a solution. In particular for the hexagons near of the pentagons. (Because, there is a tightening, and areas near the pentagons contain the most irregular hexagons sockets)

I know that with an regular hexagon I can't have a perfect result, but I want the best solution !

I'm listening to your solutions !
Thanks !

 

I am trying to make your model but getting different results. The link you posted didn't have an answer. Can you elaborate or supply a model?