It seems to me, and I am sure someone will correct me if I am wrong, that gravity inside the hollow sphere would be very interesting. All of the mass creating the gravity would be surrounding you on the outside, not the inside.
If you were just on the inside of the shell structure, there would be much more mass on the 'down' side of you from the other side (towards the center), so you would be pulled towards the equilibrium point - the center of the sphere. Would your acceleration due to gravity increase, or decrease, on the trip towards the center, as the competing forces balance out and approach equilibrium? Would you speed up in your decent towards the center, or slow down? It seems to me that, at the center, you would have no further acceleration due to gravity. All of the gravitational forces would be equalized in every direction. Would you feel them - 'weightless'?
Another point - if your unobtanium produces gravitational effects normally, through mass, your shell would have to be extremely 'massive' and therefore 'dense' in order to produce 1 g. The stresses on the shell structure would be primarily compressive. The structure, therefore, would have to be able to withstand tremendous compressive forces. This begs the question be asked, 'How compressive is the material forming the shell?', and how are these compressive forces distributed through the structure? The denser the material, the more plausible this is. However, if something very, very massive, for instance hit the planet in the center of one of your decagonal faces, would this be enough to deform the panel? The main support structures of a geodesic dome are in the connecting 'folds' between the panels. The panels themselves transfer any forces to these fold lines. Any force perpendicular to the center of the panel (towards the center of the sphere) would become a tension force. That is, the strength of a geodesic dome is in the structure of the boundaries between the panels (compressive), the folds. The actual surface of the panels themselves (tension) is the weak point. You might find that the centers of your panels deform towards the sphere center, forming concave plates, and the folds, or joints, between the plates forming ridges, or peaks. Water would flow 'downhill', from the high point of the folds/joints to the low point center of the plates. The more facets your geodesic dome has, the less this distortion would be. Perhaps 12 would be on the very low side of providing structural integrity. The closer to an infinite number of plates you get, the more it approximates a sphere, with pure compressive forces and no tension forces with a perfect distribution of material.
Now, if your 'unobtanium' creates gravity through some other mechanism than 'mass', we have a different scenario. Since 'unobtabium' is speculative in nature, could the gravitational effect be somehow related to something other than 'mass', therefore involving a completely different calculation of the stresses on the structure? This scenario makes the entire solution totally speculative in nature. In such a case anything goes. You are free to assume a perfectly rigid structure that transfers tension and compression forces perfectly, without distortion.