what geometric surface encloses the maximum volume with the minimum surface area
Surface-area-to-volume ratio For a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is the sphere, a consequence of the isoperimetric inequality in 3 dimensions. By contrast, objects with tiny spikes will have very large surface area for a given volume.
Optimal solutions for Rubik's Cube The maximum number of face turns needed to solve any instance of the Rubik's Cube is 20,[2] and the maximum number of quarter turns is 26.[3] These numbers are also the diameters of the corresponding Cayley graphs of the Rubik's Cube group. In STM (slice turn metric) it's unknown.