360 panorama mapping to polyhedron

I have created a panorama puzzle tile-rotation game which is live at panopuzzle
Screenshot: me
It maps a cube map projection of a 360 panorama onto a cube I have defined by 8 vertices. All the UV mapping to get to smaller tiles is calculated which is fairly straight forward because each side is an independent square. I can use “simple” math to create the proper UV coordinates and assign them to the tiles.
Initially I wanted (and I would still like) to use different polyhedrons - like soccer ball (truncated icosahedron) and many others (I have a library of old VRML models) BUT I can’t figure out a way to get the panoramic textures UV mapped to the separate tiles (they are all individual so I can easily rotate them).
I have the edges and vertices and all but how to map and equirectangular image (or any other projection) onto it is beyond me.
Here is an example of a grid: pano-Polyhedra2Equi
I was hoping to be able use a sphere with the texture around the polyhedron and “cut” out the tiles that way ???

Has anybody an idea on how to achieve something like that??
I know - I need to “just” write a UV mapping algorithm but that is not something I will be able to do I think - except I am missing a point and making it way to difficult for me.

Hmm - a couple of views of the question but no hints.
Not sure what that means - does it mean it is just not of interest to anybody or does it really mean it can’t be done easily??
There is a bit more of what I would like to do on stackoverflow (https://stackoverflow.com/questions/55492869/mapping-a-360-panorama-onto-a-polyhedron-in-three-js)

The problem is that I need to project the equirectangular image AND cut it.
Without the projection the piece I need will be distorted meaning a triangle will not have a straight side.
I have written a script which points the camera to the centre of each piece in a loop, mask the rest and save the image but that still doesn’t really work. I got my triangle somewhere in a black surround without “proper” coordinates

I cut those projected and saved images by hand for one instance (all pentagons) to get this:
penta_2 penta_1
but I have no idea on how to achieve that programmatically

As I mentioned before - any hint is appreciated
Perhaps somebody from the three.js team ?? @mrdoob @Mugen87 (sorry for the direct question)

Cheers

Probably the latter one. I have only seen 360 panorama apps based on equirectangular or cube projection. The first one needs a sphere, the second one a cube geometry. I’m not aware of any other approaches used in three.js.

Thanks,
the thing is - I wouldn’t mind writing some UV mapping code myself.
Problem is - is don’t really know how to combine the projection with the cutting of the tiles.
But hey - will keep on trying.