  The powerful Lagrangian view of structure formation was essentially
introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a
dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was
flat (with vanishing velocity) at the big bang. Afterward, gravity stretched
and bunched the sheet together in different places, forming a cosmic web when
projected to the position coordinates. Here, I explain some properties of an
origami approximation, in which the sheet does not stretch or contract (an
assumption that is false in general), but is allowed to fold. Even without
stretching, the sheet can form an idealized cosmic web, with convex polyhedral
voids separated by straight walls and filaments, joined by convex polyhedral
nodes. The nodes form in 'polygonal' or 'polyhedral' collapse, somewhat like
spherical/ellipsoidal collapse, except incorporating simultaneous filament and
wall formation. The origami approximation allows phase-space geometries of
nodes, filaments, and walls to be more easily understood, and may aid in
understanding spin correlations between nearby galaxies. This contribution
explores kinematic origami-approximation models giving velocity fields for the
first time.
