  The trinification grand unified theory (GUT) has gauge group SU(3)^3 and a
discrete symmetry permuting the SU(3) factors. In common with other GUTs, the
attractive nature of the fermionic multiplet assignments is obviated by the
complicated multi-parameter Higgs potential apparently needed for
phenomenological reasons, and also by vacuum expectation value (VEV)
hierarchies within a given multiplet. This motivates the rigorous consideration
of Higgs potentials, symmetry breaking patterns and alternative symmetry
breaking mechanisms in models with this gauge group. Specifically, we study the
recently proposed ``clash of symmetries'' brane-world mechanism to see if it
can help with the symmetry breaking conundrum. This requires a detailed
analysis of Higgs potential global minima and kink or domain wall solutions
interpolating between the disconnected global minima created through
spontaneous discrete symmetry breaking. Sufficiently long-lived metastable
kinks can also be considered. We develop what we think is an interesting,
albeit speculative, brane-world scheme whereby the hierarchical symmetry
breaking cascade, trinification to left-right symmetry to the standard model to
colour cross electromagnetism, may be induced without an initial hierarchy in
vacuum expectation values. Another motivation for this paper is simply to
continue the exploration of the rich class of kinks arising in models that are
invariant under both discrete and continuous symmetries.
