Hexagon
In
geometry, a hexagon is a
polygon with six edges and six vertices. Its Schl?fli symbol is .
The internal
angles of a regular hexagon are all
120?. Like squares and
equilateral triangles, regular hexagons fit together without any gaps to tile the plane , 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.
Encyclopedia
In
geometry, a
hexagon is a
polygon with six edges and six vertices. Its
Schläfli symbol is .
The internal
angles of a regular hexagon are all
120°. Like squares and
equilateral triangles, regular hexagons fit together without any gaps to tile the plane , 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 a 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 ,
truncated cuboctahedron and the
truncated icosidodecahedron.
In
French, the term
l'hexagone is often used as a nickname for
France, since the country is shaped somewhat like a hexagon.
Hexagon construction
A regular hexagon is constructible with
compass and straightedge. The following is a step-by-step animated method of this, given by
Euclid's
Elements, Book IV, Proposition 15.
External links
See also
