I'm trying to print out nets of a cube on a sheet of paper, and I'm hoping to fit as many as I can on single sheets. The squares that make up the net are $\frac{1}{2}$ an inch wide, and I'm printing on standard 8.5" x 11" printer paper. I know that all of the 11 nets of a cube can tile 2D space, but I want to find an arrangement of (possibly mixed and matched) cube nets that will cover the page as efficiently as possible with as many cubes as possible.
The best I've gotten is 55 cubes, using the arrangement below:
My hope is that there is an arrangement that can fit 60 cube nets (or some multiple of 20) on the sheet, since I plan to cut them out and tape them into a Menger Sponge. Is there such an arrangement out there?
