This article examines what role Sweden, as a presumed periphery in Northeastern Europe, played at the turn of the 1960s when Magdalena Abakanowicz and her fellow Polish artists working in fibre material broke new ground moving away from traditional tapestry by working with complex three-dimensional forms. Using the method of a history of crossing, histoire croisée, the article shows how exhibitions with Abakanowicz’s fibre art served many interests at the time, the artist’s own creative development and international career, Swedish art institutions eager to display current experimentsin soft environments, the burgeoning Swedish cultural policy making, and larger structures of cultural diplomacy. The article thus proposes to understand the relation between Sweden and Poland as two semi-peripheries, where the dominant narrative of modern art stemming from Western centres influencing the rest was, in many ways, circumvented.