SKAR81,
How you model a geodesic dome depends massively on why you are modeling it. SolidWorks does an excellent job of modeling confusion and stupidity. If the cut is difficult for you in SolidWorks, it will be difficult for the carpenter or welder or whoever.
My first thought about geodesic domes in general is that they are space frames. Space frames are ideal for maximizing access for everything in and out of the frame. This goes for you, your hands, your tools, your family, your personal belongings, rain and snow, burglars, the police, damn foreigners, animals, etc. Space frames make great jungle gyms. As shelter, a complex space frame is a way to maximize the number of seams you have to seal, somehow. A good rule for any kind of structural enclosure is that you design your covers first, then figure out the structure underneath.
Do you have to hit the diameter bang on, or you can you design a standard triangle section with rational dimensions, and hit the "diameter" approximately?
If you can design a standard connecting bracket, you can connect square cut, standard lengths of lumber, extrusion or other structural sections.
A good trick with complex frames is to create a structure shaped "blob". Make it transparent. Set the material density as low as you can. I use 0.1kg/m^3. I wish SolidWorks took into account figments of people's imaginations.
Model the blob to the outside shape that you want. Add in functional details like doors, windows, access panels, etc. Locate your geodesic pieces to the blob.
Load your blob into Custom Properties. There is a click-box that will exclude it from your bill of materials.
Your triangle section is interesting. You are aware of course that the sides of your lumber cannot be perpendicular to the faces. You might be able to do this with a table saw or circular saw, but you will need some sort of jigging procedure to make up for tolerance stack-up.
JHG