In the first paper, Alexandrov's Theorem was studied, and extended, to show that convex polyhedra form statically rigid frameworks in space, when built with plane-rigid faces. This second paper ...

Besides the regular and semiregular solids, there are just ninety-two other convex polyhedra with regular faces. In 1966, the American mathematician Norman W. Johnson, a student of H.S.M. Coxeter at ...

The works of the Greek polymath Plato have kept people busy for millennia. Mathematicians have long pondered Platonic solids, a collection of geometric forms that are highly regular and are frequently ...

Adjacency properties of extreme points of a convex polyhedron are discussed. In mathematical programming we are quite often faced with problems of characterizing the ...

In the latest verse of a centuries-old mathematical refrain, scientists have figured a way to iron out the wrinkles in a large class of molecular cages. The cages have faces consisting of 12 regular ...

Ancient Greek mathematicians – most notably Plato - classified solid shapes thousands of years ago. Since then, remarkably few geometric ‘solid’ forms have been discovered and the last collection was ...

After more than three centuries, a geometry problem that originated with a royal bet has been solved. Imagine you’re holding two equal-size dice. Is it possible to bore a tunnel through one die that’s ...