  In this paper we study Maxwell lattices with non-rectilinear constraints,
where the elastic energy is determined by the collective motion of three or
more particles, in contrast to a rectilinear spring whose elastic energy only
relies on the displacement of two particles attached to the two ends of the
spring. Utilizing polygon-shaped constraints, we found that the Maxwell
counting argument and the topological construction, based on the compatibility
matrix and the equilibrium matrix, can be generalized in our models, and our
elastic systems follow the same topological classification. In addition, we
also found that non-rectilinear constraints offers a natural pass towards
topological states with higher topological indices and multiple edge states,
which can be achieved even for a simple unit cell with one degree of freedom
per unit cell without enlarging the unit cell in the bulk or at the edge.
