Certainly not $\left(\mathop{\Large\times}_{i=1}^{2} \left[0,4-\sqrt{3}\right] \right)  \times \left( \mathop{\Large\times}_{j=3}^{k}[0,2]\right)$. 

Why not $[0,2]\times[0,4-\sqrt3\,]\times[0,4-\sqrt3\,]\times[0,2]^{k-3}$?