Hexagon
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- For other uses, see Hexagon (disambiguation).
Hexagon.png
Image:hexagon.png
A regular hexagon
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 area of a regular hexagon of side length a is given by
- <math>A = \frac{3}{2}a^2 \cot \frac{\pi}{6} = \frac{3 \sqrt{3}}{2}a^2 \simeq 2.59808 a^2.<math>
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.
HexagonConstructionAni.gif
Hexagon Construction Animation
See also
Template:Polygonsde:Sechseck es:Hexágono fr:Hexagone he:משושה ja:六角形 lt:Šešiakampis nl:Zeshoek pl:Sześciokąt pt:Hexágono sl:Šestkotnik sv:Hexagon zh:正六边形