  In a recent paper, Cristofaro-Gardiner--Li--Stanley [CGLS15] constructed
examples of irrational triangles whose Ehrhart functions (i.e. lattice-point
count) are polynomials when restricted to positive integer dilation factors.
This is very surprising because the Ehrhart functions of rational polygons are
usually only quasi-polynomials. We demonstrate that most of their triangles can
also be obtained by a simple cut-and-paste procedure that allows us to build
new examples with more sides. Our examples might potentially have applications
in the theory of symplectic embeddings.
