We study the presumably unnecessary convexity hypothesis in a theorem of Chung et al. on perimeter-minimizing planar tilings by convex pentagons. We prove that the theorem holds without the convexity hypothesis in certain special cases, and we offer direction for further research.
Ghang, Whan; Martin, Zane; and Waruhiu, Steven`
"Perimeter-minimizing Tilings by Convex and Non-convex Pentagons,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
1, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/2