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We are interested in the question of the existence of flat manifolds forwhich all $\mathbb R$-irreducible components of the holonomy representation areeither absolutely irreducible, of complex or of quaternionic type. In the firsttwo cases such examples are well known. But the existence of the third type offlat manifolds was unknown to the authors. In this article we construct such anexample. Moreover, we present a list of finite groups for which a constructionof manifolds of quaternionic type is impossible.

Flat manifolds with holonomy representation of quaternionic type