Calculations at a regular dodecagon, a polygon with twelve edges and just as many vertices.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
d6 = ( √6 + √2 ) * a
d5 = ( 2 + √3 ) * a
d4 = ( 3*√2 + √6 ) / 2 * a
d3 = ( √3 + 1 ) * a
d2 = ( √6 + √2 ) / 2 * a = d6 / 2
Height = d5
p = 12 * a
A = 3 * ( 2 + √3 ) * a²
rc = d6 / 2 = d2
ri = d5 / 2
Angle: 150°
54 diagonals
Edge length, diagonals, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
The regular dodecagon is a convex, regular polygon with twelve sides of equal length, between which there are equal angles. These angles have 150 degrees on the inside and 210 degrees on the outside. The regular dodecagon is point-symmetrical to the intersection of the diagonals over six sides, which are the longest of the five different types of diagonals. It is also axially symmetrical to these six diagonals, and it is also axially symmetrical to the six bisectors through the opposite sides. It therefore has twelve axes of symmetry.
In the first century AD, the ancient Greek mathematician Heron of Alexandria measured the area of regular polygons from the pentagon to the dodecagon and found the formulas for them, with the restriction that he used the approximate value 7/4 for the root of three, i.e. 1.75 instead of 1.732. As a result, he overestimated the area of the regular dodecagon by a little piece.
There are a few twelve-sided coins, such as the 50 cent coin from Australia. Some buildings have a twelve-sided floor plan, including the Temple of Diana in Munich's Hofgarten.
The hexagram is also a regular, albeit concave, dodecagon, but it is more associated with the number six because it has that number of points. The unicursal hexagram is also a concave dodecagon, as are the cross, the X-shape and the H-shape.