  Two dimensional modeling of collisionless shocks has been of tremendous
importance in understanding the physics of the non-linear evolution, momentum
transfer and particle acceleration, but current computer capacities have now
reached a point where three dimensional modeling is becoming feasible. We
present the first three dimensional model of a fully developed and relaxed
relativistic ion-electron shock, and analyze and compare it to similar 2D
models. Quantitative and qualitative differences are found with respect to the
two-dimensional models. The shock jump conditions are of course different,
because of the extra degree of freedom, but in addition it is found that strong
parallel electric fields develop at the shock interface, the level of magnetic
field energy is lower, and the non-thermal particle distribution is shallower
with a powerlaw index of ~2.2.
