Information about Hexagon
| Regular hexagon | |
|---|---|
) A regular hexagon, {6} | |
| Edges and vertices | 6 |
| Schläfli symbols | {6} t{3} |
| Coxeter–Dynkin diagrams | ){kind=small} ){kind=small} ){kind=small} ){kind=small} |
| Symmetry group | Dihedral (D6) |
| Area (with t=edge length) |   |
| Internal angle (degrees) | 120° |
In geometry, a hexagon is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol {6}.
Regular hexagon
)
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.
The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120° and the hexagon has 720 degrees. It has 6 lines of symmetry. 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 perimeter of a regular 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.
Hexagons: in nature and by humankind
) A beehive honeycomb | The scutes of a turtle's carapace | ) Micrograph of a snowflake | |
) Crystal structure of a molecular hexagon composed of hexagonal aromatic rings reported by Müllen and coworkers in Chem. Eur. J., 2000, 1834-1839. | ) Naturally formed basalt columns from Giant's Causeway in Ireland; large masses must cool slowly to form a polygonal fracture pattern | ) An aerial view of Fort Jefferson in Dry Tortugas National Park | ) The James Webb Space Telescope mirror is composed of 18 hexagonal segments. |
) France somehow has a hexagonal shape. In French, "L'hexagone" sometimes refers to the country. |
See also
- Hexagram - 6-sided star within a regular hexagon
- Unicursal hexagram - single path, 6-sided star, within a hexagon
- Hexagonal tiling - A regular tiling of hexagons in a plane
- Hexagonal number
External links
- Eric W. Weisstein, Hexagon at MathWorld.
- Definition and properties of a hexagon With interactive animation
- Cassini Images Bizarre Hexagon on Saturn
- Saturn's Strange Hexagon
- A hexagonal feature around Saturn's North Pole
- "Bizarre Hexagon Spotted on Saturn" - from Space.com (27 March 2007)
| Polygons |
|---|
| Triangle • Quadrilateral • Pentagon • Hexagon • Heptagon • Octagon • Enneagon (Nonagon) • Decagon • Hendecagon • Dodecagon • Triskaidecagon • Pentadecagon • Hexadecagon • Heptadecagon • Enneadecagon • Icosagon • Chiliagon • Myriagon |
edge is a one-dimensional line segment joining two zero-dimensional vertices in a polytope.
A planar closed sequence of edges forms a polygon (and a face).
..... Click the link for more information.
A planar closed sequence of edges forms a polygon (and a face).
..... Click the link for more information.
- For other uses of the word, see Vertex.
..... Click the link for more information.
In mathematics, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
The Schläfli symbol is named after the 19th-century mathematician Ludwig Schläfli who made important contributions in geometry and other areas.
..... Click the link for more information.
The Schläfli symbol is named after the 19th-century mathematician Ludwig Schläfli who made important contributions in geometry and other areas.
..... Click the link for more information.
rotation (symmetry) group of the figure.]]
The symmetry group of an object (image, signal, etc., e.g. in 1D, 2D or 3D) is the group of all isometries under which it is invariant with composition as the operation.
..... Click the link for more information.
The symmetry group of an object (image, signal, etc., e.g. in 1D, 2D or 3D) is the group of all isometries under which it is invariant with composition as the operation.
..... Click the link for more information.
dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.
..... Click the link for more information.
..... Click the link for more information.
Area is a physical quantity expressing the size of a part of a surface. The term Surface area is the summation of the areas of the exposed sides of an object.
..... Click the link for more information.
Units
Units for measuring surface area include:- square metre = SI derived unit
..... Click the link for more information.
In geometry, an interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon. A simple polygon has exactly one internal angle per vertex.
..... Click the link for more information.
..... Click the link for more information.
degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, representing 1⁄360 of a full rotation.
..... Click the link for more information.
..... Click the link for more information.
Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences.
..... Click the link for more information.
..... Click the link for more information.
POLYGONE is an Electronic Warfare Tactics Range located on the border between France and Germany. It is one of only two in Europe, the other being RAF Spadeadam.
The range, also referred to as the Multi-national Aircrew Electronic Warfare Tactics Facility (MAEWTF), is
..... Click the link for more information.
The range, also referred to as the Multi-national Aircrew Electronic Warfare Tactics Facility (MAEWTF), is
..... Click the link for more information.
- For other uses of the word, see Vertex.
..... Click the link for more information.
In mathematics, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
The Schläfli symbol is named after the 19th-century mathematician Ludwig Schläfli who made important contributions in geometry and other areas.
..... Click the link for more information.
The Schläfli symbol is named after the 19th-century mathematician Ludwig Schläfli who made important contributions in geometry and other areas.
..... Click the link for more information.
angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept
..... Click the link for more information.
..... Click the link for more information.
degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, representing 1⁄360 of a full rotation.
..... Click the link for more information.
..... Click the link for more information.
In plane (Euclidean) geometry, a square is circle with four sides.
..... Click the link for more information.
Classification
A square is a regular quadrilateral. Likewise it is also a special case of a rhombus, kite, parallelogram, and trapezoid...... Click the link for more information.
In geometry, an equilateral polygon is a polygon which has all sides of the same length.
An equilateral polygon which is convex and cyclic (its vertices are on a circle) is a regular polygon.
An equilateral triangle is a triangle of equal edge lengths.
..... Click the link for more information.
An equilateral polygon which is convex and cyclic (its vertices are on a circle) is a regular polygon.
An equilateral triangle is a triangle of equal edge lengths.
..... Click the link for more information.
A triangle is one of the basic shapes of geometry: a polygon with three corners or and three sides or edges which are straight line segments.
In Euclidean geometry any three non-collinear points determine a triangle and a unique plane, i.e.
..... Click the link for more information.
In Euclidean geometry any three non-collinear points determine a triangle and a unique plane, i.e.
..... Click the link for more information.
tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible.
..... Click the link for more information.
..... Click the link for more information.
beehive is a structure in which bees live and raise their young. A beehive is located in an apiary.
The internals of the hive comprise a densely packed matrix of hexagonal cells made of beeswax. The cells are used for storage, or for housing the brood.
..... Click the link for more information.
The internals of the hive comprise a densely packed matrix of hexagonal cells made of beeswax. The cells are used for storage, or for housing the brood.
..... Click the link for more information.
honeycomb is a mass of hexagonal wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen.
Beekeepers may remove the entire honeycomb to harvest honey. Honey bees consume about 8.
..... Click the link for more information.
Beekeepers may remove the entire honeycomb to harvest honey. Honey bees consume about 8.
..... Click the link for more information.
Voronoi diagram, named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation (after Lejeune Dirichlet), is a special kind of decomposition of a metric space determined by distances to a specified discrete
..... Click the link for more information.
..... Click the link for more information.
In geometry, a Platonic solid is a convex regular polyhedron. These are the three-dimensional analogs of the convex regular polygons. There are precisely five such figures (shown below). They are unique in that the faces, edges and angles are all congruent.
..... Click the link for more information.
..... Click the link for more information.
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical . They are distinct from the Platonic solids, which are composed of only one type of polygon meeting in identical vertices,
..... Click the link for more information.
..... Click the link for more information.
The truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 regular triangular faces, 12 vertices and 18 edges.
..... Click the link for more information.
Area and volume
The area A and the volume V of a truncated tetrahedron of edge length a are:..... Click the link for more information.
The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces, 6 regular square faces, 24 vertices and 36 edges. Since each of its faces has point symmetry the truncated octahedron is a zonohedron.
..... Click the link for more information.
..... Click the link for more information.
The truncated icosahedron is an Archimedean solid. It comprises 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.
..... Click the link for more information.
Construction
..... Click the link for more information.
Association football, commonly known as football or soccer, is a team sport played between two teams of 11 players. It is the most popular sport in the world.
..... Click the link for more information.
..... Click the link for more information.
fullerenes, discovered in 1985 by Robert Curl, Harold Kroto and Richard Smalley at the University of Sussex and Rice University, are a family of carbon allotropes named after Richard Buckminster Fuller and are sometimes called buckyballs.
..... Click the link for more information.
..... Click the link for more information.
The truncated cuboctahedron is an Archimedean solid. It has 12 regular square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges.
..... Click the link for more information.
..... Click the link for more information.
The Truncated icosidodecahedron is an Archimedean solid. It has 30 regular square faces, 20 regular hexagonal faces, 12 regular decagonal faces, 120 vertices and 180 edges.
..... Click the link for more information.
..... Click the link for more information.
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
