Hexagon

From Wikipedia, the free encyclopedia.

For other uses, see Hexagon (disambiguation).

A hexagon (also known as "sexagon") is a polygon with six edges and six vertices. Its Schläfli symbol is {6}.

The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120°. Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons.

The area of a regular hexagon of side length is given by

The circumference of an hexagon of side length is, of course, , its maximal diameter , and its minimal diameter .

There is no platonic solid made of regular hexagons. The archimedean solids with some hexagonal faces are the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron.

Hexagon construction

A regular hexagon is constructible with straightedge and compass. The following is a step-by-step animated method of this, given by Euclid's Elements, Book IV, Proposition 15.

See also

• geometry
• hexagonal number
• synthetic geometry
• hexaflexagon
• Hex map
• Magic hexagon

Polygons
Triangle | Quadrilateral | Pentagon | Hexagon | Heptagon (Septagon) | Octagon | Enneagon (Nonagon) | Decagon | Hendecagon | Dodecagon | Triskaidecagon | Pentadecagon | Heptadecagon | Enneadecagon | Icosagon | Tricontagon | Pentacontagon | Hectagon | Chiliagon | Myriagon