A model, consisting of triangular trimers on the triangular lattice is pres
ented. In analogy to the dimer problem, these particles cover the lattice c
ompletely without overlap. The model has a honeycomb structure of hexagonal
cells separated by rigid domain walls. The transfer matrix call be diagona
lized by a Bethe Ansatz with two types of particles. This leads to an exact
expression for the entropy on a two-dimensional subset of the parameter sp
ace.