Very Small Modular Hexagons: 37

Makoto Yamaguchi created the designs shown at right and similar designs below. It takes six units for the lid and six for the base, with each unit folded from a rectangular piece of paper measuring 15 cm by 7.5 cm.
 
Tomoko Fuse created the designs shown at left and similar designs below. These boxes are easy-to-make and don't use up much paper -- only two square sheets for each lid and two for each base.
 
Double-sided paper works best for all of the box styles shown here.