Polyhedron

Polyhedron

A Polyhedron is a three-dimensional shape with flat polygonal faces, straight edges, and sharp corners or vertices. The word polyhedron comes from the Classical Greek πολύεδρον, as poly- (stem of πολύς, "many") + -hedron (form of ἕδρα, "base" or "seat").

Definition

A polyhedron is a 3D analogue of a polygon. Polyhedra are the bounding solids of a finite number of half spaces. Each face is a polygon, and two faces meet along an edge which is a line segment in space. More generally, polyhedra may be defined in Euclidean space or on spheres, and may be bounded or unbounded.

Classification

Polyhedra are classified and named according to the number of sides, the kind of polygons as faces, and whether they are convex, concave or star polyhedra. The naming of polyhedra is based on the number of faces, the Greek prefix, and the suffix -hedron.

Convex polyhedra

A polyhedron is convex if its surface (comprising its faces, edges and vertices) does not intersect itself and the line segment joining any two points of the polyhedron is contained in the interior or surface. Convex polyhedra are well-defined, with several equivalent standard definitions.

Regular polyhedra

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive.

See also

• Platonic solid
• Archimedean solid
• Johnson solid
• Prism
• Antiprism
• Tessellation

External links

• Polyhedra.org

Polyhedron Resources
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