On the resolution of triangular meshes

It is generally agreed that the resolution of a regular quadrilateral
mesh is the side length of quadrilateral cells. There is less agreement
on what is the resolution of triangular meshes, exacerbated by the fact
that the numbers of edges or cells on triangular meshes are
approximately three or two times larger than that of vertices. However,
the geometrical resolution of triangular meshes, i.e. maximum
wavenumbers that can be represented on such meshes, is a well defined
quantity, known from solid state physics. These wavenumbers are related
to a smallest common mesh cell (primitive unit cell), and the set of
mesh translations that map it into itself. The wavenumbers do not depend
on whether discrete degrees of freedom are placed on vertices, cells or
edges. The resolution is defined by the height of triangles.