  We present a numerical study of the SU(N) Heisenberg model with the
fundamental representation at each site for the kagome lattice (for N=3) and
the checkerboard lattice (for N=4), which are the line graphs of the honeycomb
and square lattices and thus belong to the class of bisimplex lattices. Using
infinite projected entangled-pair states (iPEPS) and exact diagonalizations, we
show that in both cases the ground state is a simplex solid state with a
two-fold ground state degeneracy, in which the N spins belonging to a simplex
(i.e. a complete graph) form a singlet. Theses states can be seen as
generalizations of valence bond solid states known to be stabilized in certain
SU(2) spin models.
