Convex polytopes are geometric objects that look deceptively simple. They occur everywhere in mathematics and have practical applications in everyday life – like organizing your grocery shopping list. In this snapshot, you ...

The solutions to a surprising number of mathematical questions can be classified by the ADE Coxeter–Dynkin diagrams. This snapshot will show you a selection of these questions and how they correspond to the ADE Coxeter–Dynkin ...

Platonic solids have fascinated humans for thousands of years. In ancient times, they were associated with the elements fire, air, water, earth, and aether. These solids are completely symmetrical three-dimensional polyhedra. ...

This snapshot introduces the theory of trisections of smooth 4-manifolds, an area of exploration in low-dimensional topology aiming to make four-dimensional spaces more understandable. Along the way, we discuss the concepts ...

Richard Brauer (1901-1977) was a German-American mathematician who is regarded as the founder of a highly active mathematical area known as modular representation theory. This area grew from group theory, which can be ...

We describe some of the beautiful mathematical structures that arise from the study of the associativity equation. Our journey takes us from combinatorics to abstract algebra, with brief excursions through geometry and ...

Is it possible to approximate arbitrary points in space by vectors with rational coordinates, with which we, and computers, feel much more comfortable? If yes, can we approximate those points arbitrarily close? In this ...

We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the ...