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Encyclopedia > Dodecagon
A regular dodecagon.
A regular dodecagon.

In geometry, a dodecagon is any polygon with twelve sides and twelve angles. Image File history File links Dodecagon. ... Image File history File links Dodecagon. ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... Look up polygon in Wiktionary, the free dictionary. ... Look up twelve in Wiktionary, the free dictionary. ... ∠, the angle symbol. ...

Contents

Regular dodecagon

It usually refers to a regular dodecagon, having all sides of equal length and all angles equal to 150°. Its Schläfli symbol is {12}. A regular pentagon A regular polygon is a simple polygon (a polygon which does not intersect itself anywhere) which is equiangular (all angles are equal) and equilateral (all sides have the same length). ... In mathematics, the Schläfli symbol is a simple notation that gives a summary of some important properties of a particular regular polytope. ...


The area of a regular dodecagon with side a is given by:

A = 3 cotleft( frac{pi}{12} right) a^2 = 3 left( 2+sqrt{3} right) a^2 simeq 11.19615242 a^2.

Or, if R is the radius of a circumscribed circle, A black circle circumscribed by a red square In geometry, a circumscribed planar shape or solid is one that encloses and fits snugly around another geometric shape or solid. ...

A = 6 sinleft( frac{pi}{6}right) R^2 = 3 R^2.

And, if r is the radius of a inscribed circle, In geometry, an inscribed planar shape or solid is one that is enclosed by and fits snugly inside another geometric shape or solid. ...

A = 12 tanleft( frac{pi}{12}right) r^2 = 12 left( 2-sqrt{3} right) r^2 simeq 3.2153903 r^2.

Dodecagon construction

A regular dodecagon is constructible with compass and straightedge. The following is a 23 step animation illustrating one way it can be done. Notice that the compass radius is unaltered during steps 8 through 11. In mathematics, there are several notions of constructibility: a point in the Euclidean plane that can be constructed with unruled straightedge and compass. ... Creating a regular hexagon with a ruler and compass Construction of a regular pentagon Compass and straightedge or ruler-and-compass construction is the construction of lengths or angles using only an idealized ruler and compass. ...

Dodecagon Construction Animation

go eagles!!!!!!!!! Wikipedia does not have an article with this exact name. ...


Tilings

Here are 3 example periodic plane tilings that uses dodecagons: A tessellated plane seen in street pavement. ...

Tile 3bb.svg
Semiregular tiling 3.12.12
Semiregular tiling: 4.6.12
A demiregular tiling:
3.3.4.12 & 3.3.3.3.3.3

Image File history File links Tile_3bb. ... In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. ... Image File history File links Tile_46b. ... In geometry, the Great rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. ... Image File history File links Dem3343tbc. ... This article needs to be cleaned up to conform to a higher standard of quality. ...

Examples in use

  • When spelled uppercase, the outlines of the letters E and H (and I in a slab serif font) are all dodecagons.
  • The Australian 50-cent coin, Fijian 50-cent, Tongan 50-seniti, and Solomon Island 50-cent coin are regular dodecagons. Croatian 25 kuna coin has a dodecagonal shape as well. Until July 2005, a Romanian coin (5000 ROL) was also dodecagonal. The Canadian penny was dodecagonal from 1982 to 1996 as well as the South Vietnamese 20 Ðong coin till 1975. Zambian 50 ngwee (till 1992) and Malawian 50 tambala (till 1995) coins were dodecagonal. The Mexican 20 cent coin is also 12-sided.

Look up E, e in Wiktionary, the free dictionary. ... Look up H, h in Wiktionary, the free dictionary. ... Look up I, i in Wiktionary, the free dictionary. ... A sample of the Rockwell typeface, a slab serif font In typography, a slab serif (also called mechanistic, square serif or egyptian) typeface is a type of serif typeface characterized by thick, block-like serifs. ... The Australian 50 cent piece is the largest Australian coin currently issued and second largest after the Crown of 1937-38. ... “HRK” redirects here. ... For the Moldovan currency, see Moldovan leu. ... In Canada, a penny is a coin worth one cent or 1100 of a dollar. ...

See also

A dodecagonal number is a figurate number that represents a dodecagon. ... A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. ... A polyhedron (plural polyhedra or polyhedrons) is a geometric object with flat faces and straight edges. ... Look up pentagon in Wiktionary, the free dictionary. ...

External links


Dr. Eric W. Weisstein Encyclopedist Dr. Eric W. Weisstein (born March 18, 1969, in Bloomington, Indiana) is a noted encyclopedist in several technical areas of science and mathematics. ... MathWorld is an online mathematics reference work, sponsored by Wolfram Research Inc. ...

Polygons
Triangle • Quadrilateral • Pentagon • Hexagon • Heptagon • Octagon • Enneagon (Nonagon) • Decagon • Hendecagon • Dodecagon • Triskaidecagon • Pentadecagon • Hexadecagon • Heptadecagon • Enneadecagon • Icosagon • Chiliagon • Myriagon

  Results from FactBites:
 
dodecagon - definition of dodecagon in Encyclopedia (104 words)
A dodecagon is a polygon with exactly twelve sides.
When spelled uppercase, the letters E, H and I are all dodecagons.
A regular dodecagon is a dodecagon with all sides having equal length and all angles having the same number of degrees, and this number is 150.
CATHOLIC ENCYCLOPEDIA: Orvieto (894 words)
In the palace of the popes, built by Boniface VIII, is the civic museum, which contains Etruscan antiquities and works of art that are, for the greater part, from the cathedral.
Among the other notable churches of Orvieto are San Giovenale, which contains remnants of ancient frescoes, and San Andrea, which has a dodecagon tower; in 1220 Pierre d'Artois was consecrated King of Jerusalem by Honorius III in this church.
The first known Bishop of Orvieto was John (about 590), and in 591 appears a Bishop Candidus; among its other prelates were Constantino Medici, O.P., sent by Alexander IV in 1255 to Greece, where he died; Francesco Monaldeschi (1280), who did much for the construction of the cathedral.
  More results at FactBites »


 

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