  Matter density is formally infinite at the location of caustic surfaces,
where dark matter sheet folds in phase-space. The caustics separate regions
with different number of streams and the volume elements change the parity by
turning inside out when passing through the caustic stage. Being measure-zero
structures, identification of caustics via matter density fields is usually
restricted to fine-grained simulations. Here we employ a generic algorithm to
identify caustics directly using the triangulation of the Lagrangian
sub-manifold x(q,t) obtained in N-body simulations. In our approach the caustic
surfaces are approximated by a set of triangles whose vertices are particles of
the simulation. The major obstacle we encountered was insufficient sampling of
small scale perturbations. We overcame it by a brute force approach. We
continued to raise the scale of the cutoff in the initial power spectrum until
obtained the reliable resolution of the caustics shells up to seven layers.
Although quite modest, our result is the first reliable direct construction of
caustic surfaces in N-body simulation. It reveals a number of unexpected
geometrical features. In particular shapes of some of them are contrastingly
different from the known shapes of the caustics formed in the Zeldovich
approximation.
