How can I make this Dodecahedron shaped product? I'm trying to recreate this product for a client in Blender.

I really thought it would be a simple project, but I cannot figure it out!
I'm including the blend file here if it helps:

Here's how I got to this point.

I didn't see an easy way to create the Dodecahedron shape so I started with a circle and changed the number of vertices to 5.  I fill that shape in, duplicated it and tried my best to recreate the shape, merging vertices as I went.  I then used the Cast modifier to straighten out my shape and then at each vertices, I created an ico sphere.
I did try a regular sphere and also a sub-d cube, but after those attempts failed I tried an ico sphere.  I then attempted to delete the faces where the bars would connect each sphere, and would try bridge loops to connect the two spheres together.  But the angles I could never get right.  I've also tried mirror modifiers, but it's actually kind of a difficult shape that's hard to mirror and get right.
I then thought I could use the wireframe modifier on the shape and use a boolean modifer to merge with the ico spheres, it just didn't work, or at least isn't professional enough for this project.
I need to make this look as close to the product as possible, including the seams.
Any help is greatly appreciated!
Thank you!
As @Robin Betts said, Use the addon Add Mesh: Extra Objects to create the Dodecahedron.

Then in edit mode select the rouge edges that you can't use and dissolve them.

The select everything and delete only faces.
Back in object mode and convert to curve.
Now it is a curve object you can easily add roundness to the segments by increasing the bevel size, this is nice because you can come back later to change the size if you need to.

Now it's a simple matter of adding your favorite sphere shape and snapping its centre to every vertex of the dodecahedron. I recommend using ALT-D to duplicate so that if you want to change their size you can do them all at the same time.

For the seams, you could add a plane along where it needs to be, then use the knife tool to cut it up with some randomness and give it some slight thickness with a Solidify modifier and maybe a subsurf if it needs it.