  We show that the bicrossproduct model
$C[SU_2^*]{\blacktriangleright\!\!\triangleleft} U(su_2)$ quantum Poincare
group in 2+1 dimensions acting on the quantum spacetime $[x_i,t]=\imath\lambda
x_i$ is related by a Drinfeld and module-algebra twist to the quantum double
$U(su_2)\ltimes C[SU_2]$ acting on the quantum spacetime
$[x_\mu,x_\nu]=\imath\lambda\epsilon_{\mu\nu\rho}x_\rho$. We obtain this twist
by taking a scaling limit as $q\to 1$ of the $q$-deformed version of the above
where it corresponds to a previous theory of $q$-deformed Wick rotation from
$q$-Euclidean to $q$-Minkowski space. We also recover the twist result at the
Lie bialgebra level.
