Decagon

Decagon
Dimensionality	2
Schläfli Symbol	'"`UNIQ--postMath-00000001-QINU`"'
Coxeter–Dynkin diagram
Bowers acronym	dec
Subfacets
Vertices	10 points
Edges	10 line segments
Faces	1 decagon
Hypervolumes
Vertex Count	'"`UNIQ--postMath-00000002-QINU`"'
Edge Length	'"`UNIQ--postMath-00000003-QINU`"'
Surface Area	'"`UNIQ--postMath-00000004-QINU`"'

A decagon is a 2-dimensional polygon with ten edges. The Bowers acronym for a decagon is dec.

Structure and Sections

The regular decagon has each angle at 144 degrees. It can be seen as a truncated pentagon.

Hypervolumes

• vertex count = $10$
• edge length = $10l$
• surface area = $\frac{5}{2}\sqrt{5+2\sqrt{5}}l^2$

Subfacets

• 10 points (0D)
• 10 line segments (1D)
• 1 decagon (2D)

Radii

• Vertex radius: $\frac{1+\sqrt{5}}{2}l$
• Edge radius: $\frac{\sqrt{5+2\sqrt{5}}}{2}l$

Angles

• Vertex angle: 144º

Vertex coordinates

The vertices of a regular decagon of side 2 can be given by all changes of sign of:

• (1, √(5+2√5))
• ((3+√5)/2, √((5+√5)/2))
• (1+√5, 0)

Related shapes

• Dual: Self-dual
• Conjugate: Decagram
• Vertex figure: Line segment, length $\sqrt{\frac{5++\sqrt{5}}{2}}$
• Third diagonal: Length $\frac{3+\sqrt{5}}{2}$
• Fourth diagonal: Length $\sqrt{5+2\sqrt{5}}$
• Long diagoal: Length $1+\sqrt{5}$

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 $t_0 \{10\}$	Rectified $t_1 \{10\}$	Truncated $t_{0,1} \{10\}$
Decagon	Decagon	Icosagon

Regular $t_0 \{5\}$	Rectified $t_1 \{5\}$	Truncated $t_{0,1} \{5\}$
Pentagon	Pentagon	Decagon