This article raises two concerns underpinning the need for a critical history of fiber art in the 20th century. The first is a critique of aesthetic formalism predominant in the Lausanne Biennale during the 1960s and 70s, which overlooks artistic, ideological, and political milieus that drew together textile artists from localities formerly treated as peripheral in art history. The second holds to account Euro-American institutions and related historiographies for their curatorial exclusion of Arab and African fiber artists. Such inclusion, I argue, would have conjured tapestry's deeper incongruities, which emanated from unresolved questions at the core of modernism: the assigning and appropriating of artistic identities, the evaded issue of state patronage, and the persistent ideological and aesthetic problem of craft and its framing within economies. By comparing three artists: Magdalena Abakanowicz, Jagoda Buic, and Safia Farhat, I reassess New Tapestry networks, myths, and systems of state and institutional support. The circulation of Abakanowicz, Buic, and Farhat around a conflux of dimensions signals a new pathway for recovering and writing a history of fiber art, and perhaps a reflection on modernism at large.