TOPICS
Search

Regular Dodecagon

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
RegularDodecagon

The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}.

Australian 50-cent piece

The Australian 50-cent piece is dodecagonal, as illustrated above.

The inradius r, circumradius R, and area A can be computed directly from the formulas for a general regular polygon with side length a and n=12 sides,

r=1/2acot(pi/(12))
(1)
=1/2(2+sqrt(3))a
(2)
R=1/2acsc(pi/(12))
(3)
=1/2(sqrt(2)+sqrt(6))a
(4)
A=1/4na^2cot(pi/(12))
(5)
=3(2+sqrt(3))a^2.
(6)

Kűrschák's theorem gives the area of the dodecagon inscribed in a unit circle with R=1,

A=1/2nR^2sin((2pi)/n)=3
(7)

(Wells 1991, p. 137).

DodecahedronDecagon1
DodecahedronDecagon2
IcosahedronDecagon1
IcosahedronDecagon2

A plane perpendicular to a C_5 axis of a dodecahedron or icosahedron cuts the solid in a regular decagonal cross section (Holden 1991, pp. 24-25).

GreekCross
LatinCross
MalteseCross

The Greek, Latin, and Maltese crosses are all irregular dodecagons.

See also

Decagon, Dodecagon, Dodecagram, Dodecahedron, Eternity, Greek Cross, Hendecagon, Kűrschák's Theorem, Kűrschák's Tile, Latin Cross, Maltese Cross, Polygon, Regular Polygon, Trigonometry Angles--Pi/12

Explore with Wolfram|Alpha

References

Holden, A. Shapes, Space, and Symmetry. New York: Dover, 1991.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 56-57 and 137, 1991.

Cite this as:

Weisstein, Eric W. "Regular Dodecagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RegularDodecagon.html

Subject classifications