dodecagon a regular

A dodecagon is a figure geometry plane. It is a polygon with 12 vertices and sides. He has 54 diagonals and the sum of its angles is equal to 1800 ^{Regular Features Digital dodecagon}

The relationship between the side of a dodecagon and radius r of the circumscribed circle is given by

which gives as an approximation of

The area A of dodecagon regular side is given by:

Alternatively:

where r is the radius of the circumcircle.

Construction of regular dodecagon

A regular dodecagon can be constructed using a compass and a ruler. The animation below shows a 23-step way to get there. The radius of the compass is not changed between steps 8 through 11.

Paving plan using dodecagon

semi-regular tiling 3.12.12

semi-regular tessellation: 4.6.4.12

semi-regular tessellation: 3.3.4.12 & 3.3.3.3.3.3

Cutting

A clever cut a regular dodecagon in 6 shapes (pentagons or triangles) allows reassembly of parts, build a square.

Other divisions at 8, 10 or 12 pieces used to reconstruct an equilateral triangle, pentagon, decagon ...

Notes

External Links

• The square turned into dodecagon
• Dodecagon dissection of a hexagon (animated gif)

• Gate geometry

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