Spin structures of flat manifolds of diagonal type
  For each integer $d$ at least two, we construct non-spin closed oriented flat manifolds with holonomy group $\mathbb Z_2^d$ and with the property that all of their finite proper covers have a spin structure. Moreover, all such covers have trivial Stiefel-Whitney classes. 
Rafa{\l} Lutowski, Nansen Petrosyan, Jerzy Popko, Andrzej   Szczepa\'nski
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