Hexagonal Box: Separated
Hexagonal box... Purple top folded from an 8.5 inch wide hexagon gridded in 16ths... Yellow bottom folded from an 8.5 inch square divided in 7ths... It's amazing how it works out that 1/8 * 2 / root(3) is slightly larger than 1/7, thus making the top fit the bottom snugly...
The overlap section between the top and bottom is actually an anti-prism, which means the lid actually holds quite well, and does not fall off even if turned upside-down and shaken with objects inside...
The top is a result of some of the playing around I did on the yellow sheet with the offset double-pleats... It didn't look too good tessellated, but I realized the sides could be wrapped down and turned into a box-top...
Hexagonal Box: Separated
Hexagonal box... Purple top folded from an 8.5 inch wide hexagon gridded in 16ths... Yellow bottom folded from an 8.5 inch square divided in 7ths... It's amazing how it works out that 1/8 * 2 / root(3) is slightly larger than 1/7, thus making the top fit the bottom snugly...
The overlap section between the top and bottom is actually an anti-prism, which means the lid actually holds quite well, and does not fall off even if turned upside-down and shaken with objects inside...
The top is a result of some of the playing around I did on the yellow sheet with the offset double-pleats... It didn't look too good tessellated, but I realized the sides could be wrapped down and turned into a box-top...