  We propose that a simple, Lagrangian 2d $\mathcal{N}=(0, 2)$ duality
interface between the 3d $\mathcal{N}=2$ XYZ model and 3d $\mathcal{N}=2$ SQED
can be associated to the simplest triangulated 4-manifold: the 4-simplex. We
then begin to flesh out a dictionary between more general triangulated
4-manifolds with boundary and 2d $\mathcal{N}=(0, 2)$ interfaces. In
particular, we identify IR dualities of interfaces associated to local changes
of 4d triangulation, governed by the (3,3), (2,4), and (4,2) Pachner moves. We
check these dualities using supersymmetric half-indices. We also describe how
to produce stand-alone 2d theories (as opposed to interfaces) capturing the
geometry of 4-simplices and Pachner moves by making additional field-theoretic
choices, and find in this context that the Pachner moves recover abelian
$\mathcal{N}=(0,2)$ trialities of Gadde-Gukov-Putrov. Our work provides new,
explicit tools to explore the interplay between 2d dualities and 4-manifold
geometry that has been developed in recent years.
