Violet Frances

1 month ago | scientificamerican.com | Rachel Crowell |Violet Frances

When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier- sounding rhombus or trapezoid. 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). A related category, surfaces—collections of points that form boundaries in 3D space—includes an entire zoo of striking, strange mathematical objects.