The order does not matter due to swap in ρ for Intersections.

Unfortunately, the code orders the arguments to have the general set first and the AbstractPolyhedron second. This does not work here. ρ for Intersections is really ugly and would need a revision.

That said, I believe for box_approximation, there should be a workaround: the keyword argument algorithm="simple" could be passed to ρ because the simple "min" heuristics should be sufficient here. I may be wrong, but for now I sent a potential patch in #3845.

Out of ignorance and curiosity, can I ask why algorithm="simple" does not work in the general case?

It does work, but it can give arbitrarily bad approximations. After thinking about it, it probably does also in this case, so I do not think anymore that the current proposal in #3845 is a good solution.

Instead, I will probably change my proposal to defining box_approximation for Intersections and checking whether the arguments satisfy ispolyhedral, and if so, letting it create a Polyhedron.
EDIT: Done.

Below is an example showing that box_approximation is already not precise even for Intersections of bounded sets. (But here it uses another approximation algorithm based on line search.)

julia> X = Ball1(zeros(2), 1.);

julia> Y = Ball1([0.5,0], 1.);

julia> box_approximation(X ∩ Y)
Hyperrectangle{Float64, Vector{Float64}, Vector{Float64}}([0.12499999871910017, 0.0], [0.8750000012809, 0.7500000025617999])