Out of the entire infinitude of possible shapes in possible dimensions, the shapes in precisely one dimension still resisted classification. In the words of Douglas Ravenel, a mathematician at the ...

They are commonplace because we learn about two-dimensional versions of these shapes as children: triangles, squares, dodecahedrons, and other convex polygons [a polygon is any flat shape made ...

Astrophysicists say our universe might be shaped like a three-dimensional donut, meaning you could point a spaceship in one direction and eventually return to where you started.

A version of this article appears in print on Aug. 2, 2022, Section D, Page 5 of the New York edition with the headline: A.I. Predicts the Shape Of Nearly Every Protein.

Proteins belonging to a fruit fly are given shape by DeepMind’s A.I. technology. The company’s new database includes the 3-D structures for all proteins expressed by the human genome as well ...