are obtained if and only if the unit disk is a regular hexagon or a parallelogram, respectively. See also Unit disk graph Unit sphere Bieberbach conjecture References S. Golab, "Quelques problèmes métriques de la géometrie de Minkowski", Trav. de l'Acad. Mines Cracovie 6 (1932), 179. External links On the Perimeter and Area of the Unit Disc, by J.C. Álvarez Pavia and A.C. Thompson Circles 1 (number)