For objects with scalar field patterns, the cylindrical symmetry implies vertical reflection symmetry as well. However, this is not true for vector field patterns: for example, in cylindrical coordinates with respect to some axis, the vector field A = A ρ ρ ρ ρ ^ ^ + A ϕ ϕ ϕ ϕ ^ ^ + A z z ^ ^ has cylindrical symmetry with respect to the axis whenever A ρ ρ , A ϕ ϕ , and A z have this symmetry (no dependence on ϕ ϕ ); and it has reflectional symmetry only when A ϕ ϕ = 0 .