Instead, in 2017, Dr. Yao and her colleagues set out to pattern and build two-dimensional structures that could transform themselves into three-dimensional shapes.

A new 13-sided shape is the first example of an elusive "einstein" — a single shape that can be tiled infinitely without repeating a pattern.

In a breakthrough study, a research team led by Associate Professor Chae Bin Kim from the Department of Polymer Science and Engineering at Pusan National University, South Korea, developed new ...