Heptagon

Heptagon
Dimensionality	2
Schläfli Symbol	'"`UNIQ--postMath-00000001-QINU`"'
Symmetry	Heptagonal dihedral symmetry (D7)
Coxeter–Dynkin diagram
Bowers acronym	heg
Subfacets
Vertices	7 points
Edges	7 line segments
Faces	1 heptagon
Hypervolumes
Vertex Count	'"`UNIQ--postMath-00000002-QINU`"'
Edge Length	'"`UNIQ--postMath-00000003-QINU`"'
Surface Area	'"`UNIQ--postMath-00000004-QINU`"'

A heptagon is a 2-dimensional polygon with seven edges. The Bowers acronym for a heptagon is heg.

Symbols

The main Dynkin symbol of a regular heptagon is x7o.

Structure and Sections

The regular heptagon is the simplest regular polygon that can't be constructed with a compass and straightedge. Each angle is 128+4/7 degrees.

Hypervolumes

• vertex count =$7$
• edge length =$7l$
• surface area =${\frac {7}{4}}\cot \left({\frac {\pi }{7}}\right){l}^{2}$

Subfacets

• 7 points (0D)
• 7 line segments (1D)
• 1 heptagon (2D)

Radii

• Vertex radius:${\frac {1}{2\sin({\frac {\pi }{7}})}}l$
• Edge radius:${\frac {1}{2\tan({\frac {\pi }{7}})}}l$

Angles

• Vertex angle: ${\frac {900}{7}}$°

Related shapes

• Vertex figure: Line segment, length$2\cos({\frac {\pi }{7}})$
• Dual: Self-dual

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 $t_{0}\{7\}$	Rectified $t_{1}\{7\}$	Truncated $t_{0,1} \{ 7 \}$
Heptagon	Heptagon	Tetradecagon