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 ...

Wheeler’s more ingenious plane dissections involved polyhedra, cut into smaller polyhedra, that could then be rearranged to form other polyhedra. He and his students first made these models of paper.

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 distinctive three-dimensional shape in Albrecht Dürer’s 1514 engraving Melencolia I has been the subject of innumerous analyses and still no one is sure what it is or what it means. On the ...

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 ...

The flat faces and straight edges of a cube signify that it belongs to a large family of geometric shapes known as polyhedra. Several years ago, mathematician John H. Conway of Princeton University ...