Buckyballs are popular shapes for geodesic domes.
All the edges have the same length and only one type of vertex.
The each vertex connects two hexagons with one pentagon.
A real dome is going to be more complicated because you will want more floor area than one face.
Joining or extending balls is harder again because most faces are at strange angles.
Here is one way to add an extension.
There are simpler ways but this keeps the faceted look of the dome.
The end of the tube part could be repeated as desired.
Instead of a single dome more could be added as required. The most likely use would be as a greenhouse or shade house.

Also I'm uploading some fused bucky balls to show how a cluster can be made.

I should point out these shape are not exact. I'm using sketchup which is lousy for this kind of thing.