https://www.kirkusreviews.com/book-reviews/paul-steinhardt/the-second-kind-of-impossible/

An admirable popular account of the quasicrystal, an oddball arrangement of atoms that seems to contradict scientific laws. Steinhardt (Physics and Astrophysical Sciences/Princeton Univ.; co-author: Endless Universe: Beyond the Big Bang, 2006), a pioneer in the field and a fine writer, makes a mighty effort to describe a complex chemical phenomenon; he mostly succeeds. Readers should carefully read his explanation of how pure substances such as minerals form periodic, symmetric arrangements of atoms called crystals, which must fit together with no gaps into which other atoms can squeeze. Only three forms qualify: the tetrahedron, the triangular prism, and the parallelepiped (six-sided box). Popular writers use the tiling analogy. To install a bathroom floor, only square, triangular, or hexagonal tiles fit perfectly. Just as you can’t fit pentagonal or octagonal tiles into the floor, no crystal can have five or eight or any larger-sided symmetry. This was the rule—not really a formal law—until Roger Penrose invented Penrose tiles in the 1970s. These can fill any room despite having bizarre shapes. Intrigued, scientists began producing five, eight, and other many-sided “quasicrystals” by heating and rapidly cooling metals in the laboratory. Thankfully, Steinhardt turns his attention from crystal theory to chronicle a gripping scientific quest. He and his colleagues searched the world’s mineralogical collections, drawing a blank until minuscule specks from Italy showed promise. Proof required finding similar pieces in a natural location, an exhaustive 10-year process that began with frustrating detective work to discover the specimen’s source, followed by an expedition to Siberia and success in 2009. Scientists figured out that natural quasicrystals form through temperatures and pressures that don’t exist on Earth; they’re found in meteorite fragments. The research continues, and it will hopefully produce technological marvels (or maybe not). Meanwhile, readers will enjoy this enthusiastic introduction to a weird but genuine new form of matter.