You can make families of large Platonic solids with triangular faces (deltahedra), made sturdy by `creasing' their edges to become dome-like. The shapes that results are all deltahedra, and although the principles of construction are similar, very few are Lobel frames (presumably since they cannot be cut in a straight manner to make them architecturally interesting). There are three parameters to each family member: The sum of those last two parameters determines the edge length of the result.