Puzzle of the Week #136 - Packing 31 Shapes in the Space of 25

This would work well as a physical puzzle, if someone wants to have a go at making it.

You have a number of identical objects whose edges are two equal circular arcs. Since each of the shaped is 12cm long and 4cm wide, 25 of them completely fill a 12 x 100 tray as shown.

However it is possible to rearrange them and fit in extra shapes. The very surprising fact is that you can fit SIX extra shapes in. Obviously none of the shapes can overlap each other, or the edges of the box. And you cannot cut the shapes up into smaller pieces.

new packing.JPG

How is this possible!?