Breakthrough origami algorithm builds 3D objects with minimal polygons

For Professor Eric Dayman, this was a lifelong commitment. Back in 1999, he developed the first universal method of transforming a sheet of paper into a three-dimensional shape, but was horrified at the sight of the final result. Too many seams and joints, plus an extremely irrational consumption of material. But can you do better? A real challenge for a mathematician, and it was accepted.

After 18 years of work, an incredibly complex, but beautiful and comprehensive algorithm for constructing absolutely any three-dimensional object was created. In spirit, it is close to origami - you take a simple flat sheet and fold it a certain number of times to get a three-dimensional multifaceted figure. Nothing is cut, does not stick together, the paper is only bent, and now the minimum number of times.

The key advantage of Professor Dayman's algorithm is its versatility. In early works, everything worked out easily if the starting material was a long thin strip that was easy to fold. But the square sheet baffled the developers and what was easy to imagine in theory looked terrible in practice. Now the opposite is true - you will hardly be able to explain the algorithm "on the fingers", but it is easy to implement in modern computing systems.

The algorithm is in essence an abstract thing, but it has bright prospects for practical application. Imagine a cheap robot with conventional manipulators that can fold anything from a sheet of composite material. From a kayak to a soldier's helmet, from a car door to an ISS part - no seams, no fasteners, no waste of material.