  Cold primordial particle dark matter forms with a distribution in
six-dimensional phase space closely approximating a three-dimensional sheet.
Folds in the mapping of this sheet onto configuration space create ubiquitous
sheetlike caustics (``micropancakes''). A typical WIMP dark matter halo has
many micropancakes, each with a scale comparable to the halo itself, a width
about $10^{-8}$ of the halo size and a typical maximum density up to about
$10^4$ times the halo mean. It is demonstrated here that the total annihilation
rate of dark matter particles is dominated by particles close to these
micropancakes, so radiation is emitted predominantly from highly contorted
two-dimensional surfaces rather than a filled volume. The total annihilation
rate of particles is about a factor of 5 higher than predicted from N-body
simulations, which cannot resolve these features. Micropancakes also produce
sharp line discontinuities in the surface brightness of annihilation radiation.
