Explore: Convex Polyhedra

The convex polyhedra are a well defined class of polyhedra with several equivalent standard definitions. Every convex polyhedron is the convex hull of

be categorized as elementary polyhedra, meaning they cannot be separated by a plane to create two small convex polyhedra with regular faces. The first

of edges or the angles between edges or faces.) Notable eight-sided convex polyhedra include: Hexagonal prism: Two faces are parallel regular hexagons;

Oriented matroid Nef polyhedron Steinitz's theorem for convex polyhedra Branko Grünbaum, Convex Polytopes, 2nd edition, prepared by Volker Kaibel, Victor

Convex Polyhedra is a book on the mathematics of convex polyhedra, written by Soviet mathematician Aleksandr Danilovich Aleksandrov, and originally published

reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms

The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative integer-valued solutions does a system of linear

possible cube that can pass through a hole in a unit cube. Many other convex polyhedra, including all five Platonic solids, have been shown to have the Rupert

vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is, every convex polyhedron forms a 3-connected

have been responsible for the first known proof that no other convex regular polyhedra exist. The Platonic solids are prominent in the philosophy of Plato