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Background: Many different shape degrees of freedom play crucial roles in determining the nuclear ground state and saddle point properties and the fission path. For the study of nuclear potential energy surfaces, it is desirable to have microscopic and self-consistent models in which all known important shape degrees of freedom are included.Purpose: By breaking both the axial and the spatial reflection symmetries simultaneously, we develop multidimensionally-constrained relativistic mean field (MDC-RMF) models.Methods: The nuclear shape is assumed to be invariant under the reversion of x and y axes, i.e., the intrinsic symmetry group is V4 and all shape degrees of freedom β λµ with even µ, such as β20, β22, β30, β32, β40, . . . , are included self-consistently. The single-particle wave functions are expanded in an axially deformed harmonic oscillator (ADHO) basis. The RMF functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the nonlinear or density-dependent couplings. The pairing effects are taken into account with the BCS approach.Results: The one-, two, and three-dimensional potential energy surfaces of 240 Pu are illustrated for numerical checks and for the study of the effect of the triaxiality on the fission barriers. Potential energy curves of even-even actinide nuclei around the first and second fission barriers are studied systematically. Besides the first ones, the second fission barriers in these nuclei are also lowered considerably by the triaxial deformation. This lowering effect is independent of the effective interactions used in the RMF functionals. Further discussions are made about different predictions on the effect of the triaxiality between the macroscopic-microscopic and MDC-RMF models, possible discontinuities on PES's from self-consistent approaches, and the restoration of broken symmetries.Conclusions: MDC-RMF models give a reasonably good description of fission barriers of even-even actinide nuclei. It is important to include both the nonaxial and the reflection asymmetric shapes simultaneously for the study of potential energy surfaces and fission barriers of actinide nuclei and of those in unknown mass regions such as, e.g., superheavy nuclei.PACS numbers: 21.60. Jz, 24.75.+i, 27.90.+b

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