Extended Data Fig. 6. 3D computational vertex model and simulation protocol.

a, Discretization of the tissue: the thick lines denote the intersection between cellular faces and the thin lines the triangulation of the cell surfaces. b, Pattern of apical, basal and lateral surface tensions prescribed in the initial regular cell monolayer. c, Equilibration of the initial regular monolayer with patterned surface tensions on a rigid substrate, where basal nodes are constrained to a plane but can slide horizontally. Initial state (i), equilibrated state (ii), and different view of equilibrated state with basal cell outline (iii). d, Coupling with a deformable substrate, modeled computationally with a tetrahedral mesh discretizing a hyperelastic block (i). The equilibrated crypt on a rigid substrate (c-ii) is further equilibrated on the deformable substrate (d-ii,iii).