Here are all planar hexaspheres. The set is the union of the 82 pentahexes and the 35 hexominoes with the straight piece in both sets. So we get 116 different pieces.
The 82 hexagonal pieces can be packed in a 8x16 roof, but a first attempt to fill the whole
figure failed. Then I split up the construction into a smaller roof and three planar polygons with hexagonal structure. At first the roof was filled saving pieces with good tilability and at last only some truncated trapeziums had to be packed.
With all planar pieces two 8x12 roofs are possible to construct. Because the hexominoes are in the set it is somewhat easier to fill the orthogonal structure at the bottom of the roof.
You can find the other constructions at my 100+ gallery.