  In this paper, we propose a simple generalization of the locally r-symmetric
Jordanian twist, resulting in the one-parameter family of Jordanian twists. All
the proposed twists differ by the coboundary twists and produce the same
Jordanian deformation of the corresponding Lie algebra. They all provide the
$\kappa$-Minkowski spacetime commutation relations. Constructions from
noncommutative coordinates to the star product and coproduct, and from the star
product to the coproduct and the twist are presented. The corresponding twist
in the Hopf algebroid approach is given. Our results are presented symbolically
by a diagram relating all of the possible constructions.
