Wheeler and his students made some models of polyhedra divided into smaller polyhedra, often of equal size and shape, without attempting to transform the pieces into other polyhedra. Geometric Model ...

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 ...

Consider what happens when a vertex of one tetrahedron pierces the face of a second tetrahedron to form a new, more complicated polyhedron. In the resulting geometric form, one triangular face has a ...

Combinatorial geometry, an area intertwining discrete mathematics and geometry, investigates the structure, properties and interrelations of polytopes—multidimensional generalisations of polygons and ...

The shapes of surfaces captured the imagination and attention of many mathematicians in the 19th century. To unfold the visual secrets compressed and hidden within the shorthand of algebraic ...

Lattice-free sets a n d their applications for cutting-plane methods in mixed-integer optimization have been studied in recent literature. The family of all integral lattice-free polyhedra that are ...

To generations of schoolchildren, myself included, the name of HSM Coxeter stood for the wonder of geometry. The spectacular images - polyhedra radiating out in star shapes, and rotating rings of ...

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 ...