[fjmokvwc] Packings, coverings, partitions

• Pack N congruent discs into a shape.  Maximize disc area.
• Cover a shape with N overlapping congruent discs.  Minimize disc area.  Previously, constellations.
• Divide a shape into N regions of equal area, minimizing perimeter.
• 3D and higher dimensions.

On a curved manifold, a circle or disc is defined by a center and distance function.

Inspirations: "Partitions of Minimal Length on Manifolds" (Beniamin Bogosel and Edouard Oudet), "The minimal perimeter for N confined deformable bubbles of equal area" (S.J. Cox and E. Flikkema)

The perimeter-minimizing equal-area partition of the surface of a sphere for a given N would be nice as a physical model, though it would take some thought to 3D print because 3D printers typically don't do colors.  Surface of a cube or box is easier: just glue pre-printed paper illustrating the partitions onto the faces.