{| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Regular hexagon
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|align=center colspan=2|
A regular hexagon
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|bgcolor=#e7dcc3|Edges and vertices||6
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|bgcolor=#e7dcc3|Schläfli symbols||{6}
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|bgcolor=#e7dcc3|Coxeter–Dynkin diagrams|||-
|bgcolor=#e7dcc3|Symmetry group||Dihedral (D₆)
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|bgcolor=#e7dcc3|Area
(with t=edge length)||$A\; =\; \backslash frac\{3\; \backslash sqrt\{3\}\}\{2\}t^2$$\backslash simeq\; 2.598076211\; t^2.$
|-
|bgcolor=#e7dcc3|Internal angle
(degrees)||120°
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|bgcolor=#e7dcc3|Properties||convex, cyclic, equilateral, isogonal, isotoxal
|}

In geometry, a hexagon is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol {6}.

Regular hexagon

The internal angles of a regular hexagon (where all of the sides are the same) are all 120° and the hexagon has 720 degrees T. It has 6 rotational symmetries and 6 reflection symmetries, making up the dihedral group D₆. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice its sides in length. 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 $t\backslash ,\backslash !$ is given by
$A\; =\; \backslash frac\{3\; \backslash sqrt\{3\}\}\{2\}t^2\; \backslash simeq\; 2.598076211\; t^2.$
Also, it can be found by the formula A=ap/2, where a is the apothem and p is the perimeter.

The perimeter of a regular hexagon of side length $t\backslash ,\backslash !$ is, of course, $6t\backslash ,\backslash !$, its maximal diameter $2t\backslash ,\backslash !$, and its minimal diameter $t\backslash sqrt\{3\}\backslash ,\backslash !$.

Related figures

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A regular hexagon can also be created as a truncated equilateral triangle, with Schläfli symbol t{3}. This form only has D₃ symmetry. In this figure, the remaining edges of the original triangle are drawn blue, and new edges from the truncation are red.
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The hexagram can be created as a stellation process: extending the 6 edges of a regular hexagon until they meet at 6 new vertices.
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A concave hexagon
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A self-intersecting hexagon
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Petrie polygons

The regular hexagon is the Petrie polygon for four higher dimensional polytopes, shown in these skew orthogonal projections:

Polyhedra with hexagons

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.

And 9 Johnson solids:

• triangular cupola, elongated triangular cupola, gyroelongated triangular cupola, augmented hexagonal prism, parabiaugmented hexagonal prism, metabiaugmented hexagonal prism, triaugmented hexagonal prism, augmented truncated tetrahedron, triangular hebesphenorotunda

Regular and uniform tilings with hexagons

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The hexagon can form a regular tessellate the plane with a Schläfli symbol {6,3}, having 3 hexagons around every vertex.
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A second hexagonal tessellation of the plane can be formed as a truncated triangular tiling, with one of three hexagons colored differently.
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A third tessellation of the plane can be formed with three colored hexagons around every vertex.
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|Trihexagonal tiling
|Trihexagonal tiling
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|Rhombitrihexagonal tiling
|Truncated trihexagonal tiling
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Hexagons: natural and human-made

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

• Hexagonal crystal system