Geodesic dome - GeometryGym

I made geodesic dome using plugin GeometryGym.

https://geometrygym.wordpress.com/downloads/

I have two problem:

1. How create surfaces from lines? First ball has got faces because of extrusion, but what with inner ball made from hexagons?

2. What if i want triangles to be convex? How to create surfaces like that? 

Thank you for your help!