Smallest Nanodots Hollow Cube (hexahedron) 24 Dots

This would be the smallest possible hollow cube. It is made up by using 4 dots squares on each of the 6 sides. The total dots required is 24 dots.

It is actually a hexahedron, which is a 6 six sided polyhedron.

Nanodots Small Sphere (dodecahedron) 60 Dots

This is one of the smaller sphere (based on a dodecahedron)  that you could make with your Nanodots. It requires 60 dots of which are 12 hexagons of 5 dots rings each.