This paper was inspired by empirical encounters with students and teacher-administrators who engaged with an online European education initiative, which raised questions about whether and how their practices were situated as local, transnational, or national(ist) endeavors. The conceptual, theoretical, and methodological resources of social topology and critical border studies guided our inquiry by a focus on bordering practices and how these generate spatiotemporal forms and movements, and evoked a "typical national form" which is characterized as a singular, stable, linear, and flat "topography." An innovative methodology is deployed to scrutinize how practices with this online, European initiative continue, challenge or complement that typical national form. The findings demonstrate how the use of topographical indexes and tropes (re-)materialized characteristics of these typical national forms, while the combination with topological relations introduced multiplicities and "levels" in these forms. Moreover, spherical forms, bouncing movements, and tunneling movements challenged the singularity, stability, linearity, and flatness of the typical national form. Building on these findings, the paper sets forth the argument that this online European education initiative mainly challenges the enactment of nationalism in classrooms by encouraging learning and thinking through "translocalities," which accentuates distances and differences that are being crossed without appealing to the typical imaginary of the "nation" with linear, stable, flat borders.