polyhedra dodecahedron platonic solids solid modeling shapes tetrahedron

Hi! I want to create a connector for a dodecahedron and I have no clue how I can realize the many rotations that are needed to make it work. Here is the geometry that I want to translate/rotate: And in the end it should be something like this: Can you point me in a direction, which tools I should use for that? Thanks in…