Offset curve along cube?

Hi guys and girls im pretty new to Rhino and Grasshopper.

I got a little problem i have some curves on my cube and want to make an offset arround the cube so that i can unroll them later and make a lasercut.

Im having a lot of trouble to make the offset along the surface of the cube.

Someone got an idea?

At the end there should be many cubes with different density of the outer net crossing each other.

It´s kind of

around a cube

Kind Regards Pascal

CUBEFraming.3dm (113.0 KB) (14.1 KB)