Sauwastika, 2021

THIS IS NOT THE NAZI'S SYMBOL!!

The Sauwastika (or Sauvastika), is a traditional symbol in Hinduism and Buddhism. Since the Tang dynasty of China, its meaning has been officially defined as "the crossroad of all the good fortunes and virtues". Its mirror image (the Swastika), when tilted, is unfortunately used by the most notorious madman in history to symbolize terror and hatred and has since lead to so many misunderstandings of this symbol. But this symbol existed thousands of years before the Nazis and is still used in the eastern culture with its original meaning.

Back in 2014, I designed my first version of this icon, but it was very inefficient: it was done simply by creating four long flaps and make a fold on each of them, wasting the paper at the joints. it is also quite difficult to fully absorb the unused area at the center of the sheet, so I used those to make a water lily (also a common symbol of Buddhism) at the middle of the model, which is not a bad utilization, but still, I was hoping to get the plain version of this symbol with the optimal efficiency.

Only until recently, as I discuss my theory of the edge-river method (ERM) with other folders on Discord I recall this old design challenge of mine. With the strength of ERM, I can finally solve this puzzle. (The following discussion uses ERM terminology and conventions, which I will explain in the future article.)

This is the abstraction. A quick counting shows the optimal grid size should be 20\times 20. Yet a feasible arrangement of lakes turned out to be really tricky. After trying various possibilities, I settled with the following solution.

This solution involves a tricky twisting river structure around the center, which is equally tricky to collapse. The pytha variation near the corner serves two purposes: to make room for the nearby level shifter and to create a small flap that enables us to lock the loose layer at the joint. The CP is shown as follows.