Here are CP’s for the complete set of shapes “Icosahedra with One or More Slices Cut Out of Them, Whose Faces are Composed of Pentagons and Triangles.” I have not yet tried to fold any of these yet, but the layouts all look doable. As luck would have it, I picked a good reference point (half the distance from the edge of the paper to the center) to begin developing the CP for the three-pentagon shape, and can readily develop the other shapes with the same edge length. Four out of the five are remarkably efficient! However the smallest of them, the pentagonal pyramid, wastes a lot of paper. I ought to find a good smaller size sheet to use for that.