Convexity conditions for growth forms in nonregular grid tilings

Characterize the precise conditions under which nonregular grid tilings yield convex versus nonconvex growth forms.

Background

While regular grid tilings have convex growth forms described by projections of orthoplexes, nonregular grids can exhibit nonconvex growth forms. The authors note uncertainty regarding the criteria that govern convexity in these settings.

A characterization would extend the current theory beyond regular grids, delineating structural features that produce nonconvex growth behavior.