I have been trying to make a 3D model like  in Cinema 4D, but with no success. How can a graphic like this be made and is there a better program for it?
Cinema 4D will definitely give you the result you're after.
You can make your geometric shape the way joojaa suggested. A sphere set to Type: Icosahedron and Segments set to <10 will work similarly to a platonic shape. Make the object Editable, then randomly select vertices all around the object, and either move them one by one, or select multiple vertices and use the scale tool to scale them out uniformly.
To get the very faceted look of this polygon, go to the Object Manager and delete the phong tag next to the object (icon with two brown spheres diagonal from each other).
Next, copy the object. Without moving it, scale the copy up so that it is slightly larger than the original (you will no longer see the original as it is inside the copy). Create an Atom Array object and drag the copy so that it is a child of the Atom Array. You can play with the scale of the cylinders and spheres in the Atom Array attributes.
Adding some simple materials and lights will get you something like this:
Mostly any 3D application will do. For practical purposes you may want to start of with a Icosaherdon, or a dodecaedron . then just randomly move the points about. Copy mesh offset make struts, spheres and render.
 Platonic solids, Wikipedia