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Hexagons

Regular hexagon
Regular polygon 6 annotated.svg
A regular hexagon
Type Regular polygon
Edges and vertices 6
Schläfli symbol {6}, t{3}
Coxeter diagram CDel node 1.pngCDel 6.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node 1.png
Symmetry group Dihedral (D6), order 2×6
Internal angle (degrees) 120°
Dual polygon Self
Properties Convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six sided polygon or 6-gon. The total of the internal angles of any hexagon is 720°.

A regular hexagon has Schläfli symbol {6} and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges.

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

The common length of the sides equals the radius of the circumscribed circle, which equals times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has 6 rotational symmetries (rotational symmetry of order six) and 6 reflection symmetries (six lines of symmetry), making up the dihedral group D6. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.


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Wikipedia

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