The problem you're describing is kind of dual to the problem with parametrized representations. It's easy to construct parametrized boundary representations (a

The problem you're describing is kind of dual to the problem with parametrized representations. It's easy to construct parametrized boundary representations (as OP used) that maintain topological invariants, but it's very difficult to use them to explore the space of possible topologies (which would be relevant if OP wanted to say, design a lighter wheel).