  Background: The relativistic three-body problem has a long tradition in
few-nucleon physics. Calculations of the triton binding energy based on the
solution of the relativistic Faddeev equation in general lead to a weaker
binding than the corresponding non-relativistic calculation. Purpose: In this
work we solve for the three-body binding energy as well as the wave function
and its momentum distribution. The effect of the different relativistic
ingredients are studied in detail. Method: Relativistic invariance is
incorporated within the framework of Poincar{\'e} invariant quantum mechanics.
The relativistic momentum-space Faddeev equation is formulated and directly
solved in terms of momentum vectors without employing a partial-wave
decomposition. Results: The relativistic calculation gives a three-body binding
energy which is about 3% smaller than its non-relativistic counterpart. In the
wave function, relativistic effects are manifested in the Fermi motion of the
spectator particle. Conclusions: Our calculations show that though the overall
relativistic effects in the three-body bound state are small, individual
effects by themselves are not necessarily small and must be taken into account
consistently.
