Just as the sphere offered an alternative to a flat Earth, other three-dimensional shapes offer alternatives to “ordinary” infinite space. We can ask two separate but interrelated questions about the ...

But to mathematicians, shapes encompass a vast universe of surprising forms, from one-dimensional loops to polytopes (geometric objects with flat sides that can exist in any desired dimension).

Hard as it may be to imagine, there’s a newly defined geometric shape ... specific polygonal shapes such as triangles, squares, and hexagons can arrange to cover a 2D plane without any gaps.

“A central problem of geometry is the tiling of space ... However, many tilings in nature are characterized by shapes with curved edges, non-flat faces, and few, if any, sharp corners.

Kirigami is a traditional Japanese art form that entails cutting and folding paper to produce complex three-dimensional (3D) ...

A quartet of mathematicians from Yorkshire University, the University of Cambridge, the University of Waterloo and the University of Arkansas has discovered a 2D geometric shape that does not ...