Regular polygon

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Area (with side length s {\displaystyle s} )

A = 1 4 n s 2 cot ⁡ ( π n ) {\displaystyle A={\tfrac {1}{4}}ns^{2}\cot \left({\frac {\pi }{n}}\right)}

Circumscribed circle diameter

d OC = s csc ⁡ ( π n ) {\displaystyle d_{\text{OC}}=s\csc \left({\frac {\pi }{n}}\right)}

Dual polygon

Self-dual

Edges and vertices

n {\displaystyle n}

Inscribed circle diameter

d IC = s cot ⁡ ( π n ) {\displaystyle d_{\text{IC}}=s\cot \left({\frac {\pi }{n}}\right)}

Internal angle

( n − 2 ) × π n {\displaystyle (n-2)\times {\frac {\pi }{n}}}