Hexagon

A hexagon is a 2-dimensional polygon with six edges. The Bowers acronym for a hexagon is hig. It is one of the regular polygons that can tile 2-D space forming the hexagonal tiling, unlike pentagons, which cannot tile the plane. Hexagons have the greatest numbers of edges and angles of any regular polygon that can tile the plane.

Symbols[]

Dynkin symbols for the hexagon include:

x6o (regular)
x3x (ditrigon)
ho3oh&#zx (triambus)
xu ho&#zx (rectangle symmetry)
xux&#xt
ohho&#xt

Structure and Sections[]

The regular hexagon has equal edge lengths and each angle as 120 degrees. It can be seen as a truncated triangle.

Hypervolumes[]

vertex count = $6$
edge length = $6l$
surface area = ${\frac {3{\sqrt {3}}}{2}}{l}^{2}$

Subfacets[]

6 points (0D)
6 line segments (1D)
1 hexagon (2D)

Radii[]

Vertex radius: $l$
Edge radius: $\frac{\sqrt{3}}{2}l$

Angles[]

Vertex angle: 120º

Vertex coordinates[]

The vertex coordinates of a regular hexagon of side 2 are:

(±1,±√3)
(±2,0)

Related shapes[]

Dual: Self dual
Vertex figure: Line segment, length $\sqrt{3}$ (short diagonal)
Long diagonal: Line segment of length 2

See Also[]


$\{0\}$	$\{1\}$	$\{2\}$	$\{3\}$	$\{4\}$	$\{5\}$	$\{\frac{5}{2}\}$	$\{6\}$	$\{7\}$	$\{\frac{7}{2}\}$	$\{\frac{7}{3}\}$	$\{8\}$	$\{\frac{8}{3}\}$	$\{9\}$	$\{\frac{9}{2}\}$	$\{\frac{9}{4}\}$	$\{10\}$	$\{\frac{10}{3}\}$	$\{11\}$	$\{\frac{11}{2}\}$	$\{\frac{11}{3}\}$	$\{\frac{11}{4}\}$	$\{\frac{11}{5}\}$	$\{12\}$	$\{\frac{12}{5}\}$	$\{13\}$	$\{\frac{13}{2}\}$	$\{\frac{13}{3}\}$	$\{\frac{13}{4}\}$	$\{\frac{13}{5}\}$	$\{\frac{13}{6}\}$	$\{14\}$	$\{\frac{14}{3}\}$	$\{\frac{14}{5}\}$	$\{15\}$	$\{\frac{15}{2}\}$	$\{\frac{15}{4}\}$	$\{\frac{15}{7}\}$	$\{16\}$	$\{\frac{16}{3}\}$	$\{\frac{16}{5}\}$	$\{\frac{16}{7}\}$	$\{17\}$	$\{\frac{17}{2}\}$	$\{\frac{17}{3}\}$	$\{\frac{17}{4}\}$	$\{\frac{17}{5}\}$	$\{\frac{17}{6}\}$	$\{\frac{17}{7}\}$	$\{\frac{17}{8}\}$	...	$\{\infty\}$	$\{x\}$	$\{\frac{\pi i}{\lambda}\}$
Zerogon	Monogon	Digon	Triangle	Square	Pentagon	Pentagram	Hexagon	Heptagon	Heptagram	Great heptagram	Octagon	Octagram	Enneagon	Enneagram	Great enneagram	Decagon	Decagram	Hendecagon	Small hendecagram	Hendecagram	Great hendecagram	Grand hendecagram	Dodecagon	Dodecagram	Tridecagon	Small tridecagram	Tridecagram	Medial tridecagram	Great tridecagram	Grand tridecagram	Tetradecagon	Tetradecagram	Great tetradecagram	Pentadecagon	Small pentadecagram	Pentadecagram	Great pentadecagram	Hexadecagon	Small hexadecagram	Hexadecagram	Great hexadecagram	Heptadecagon	Tiny heptadecagram	Small heptadecagram	Heptadecagram	Medial heptadecagram	Great heptadecagram	Giant heptadecagram	Grand heptadecagram	...	Apeirogon	Failed star polygon ($x$-gon)	Pseudogon ($\frac{\pi i}{\lambda}$-gon)


Regular $t_0 \{6\}$	Rectified $t_1 \{6\}$	Truncated $t_{0,1} \{6\}$
Hexagon	Hexagon	Dodecagon


Regular $t_0 \{3\}$	Rectified $t_1 \{3\}$	Truncated $t_{0,1} \{3\}$
Triangle	Triangle	Hexagon


Regular $t_0 \{\frac{6}{5} \}$	Rectified $t_1 \{\frac{6}{5} \}$	Truncated $t_{0,1} \{\frac{6}{5} \}$
Hexagon	Hexagon	Dodecagram