Dodecagon
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A Dodecagram is a polygon with twelve edges and angles
 Polygrams
121  122  123  124  12 
 Petrie Polygons
A_{11}
11simplex  Rectified 11simplex  Birectified 11simplex  Trirectified 11simplex  Quadrirectified 11simplex  Quintirectified 11simplex 
BC_{6}
6orthoplex  Rectified 6orthoplex  Birectified 6orthoplex  Birectified 6cube  Rectified 6cube  6cube 
D_{7}
t_{5}(1_{41})  t_{4}(1_{41})  t_{3}(1_{41})  t_{2}(1_{41})  t_{1}(1_{41})  t_{0}(1_{41}) 
E_{6}
t_{0}(2_{21})  t_{1}(2_{21})  t_{1}(1_{22})  t_{0}(1_{22}) 
F_{4}
24cell  Rectified 24cell  Snub 24cell 
 Information
 The Dodecagon has 12 Edges and Verticies
 Its Schläfli Symbol is {12}
 Its Coxeter Diagram is
 Its Symmetry Group is D_{12}, order 2x12
 cyclic, convex, equilateral, isogonal, isotoxal
 (Where is the radius of the circumscribed circle.)
 One internal is 150°
 All internal angles added up is 1,800°
 Dual Polygon: Itself
 Propertires: convex, cyclic, equilateral, isogonal, isotoxal
 54 Diagonals and 10 different triangles made from diagonals
 Real Life Examples
 In block capitals, the letters H, X and E(and I in a slab serif font) have dodecagonal outlines.
 The regular dodecagon features prominently in many buildings. The Torre del Oro is a dodecagonal military watchtower in Seville, southern Spain, built by the Almohad dynasty. The early thirteenth century Vera Cruz church in Segovia, Spain is dodecagonal. Another example is the Porta di Venere (Venus' Gate), in Spello, Italy, built in the 1st century BC has two dodecagonal towers, called "Propertius' Towers".
 Regular dodecagonal coins include:
 British threepenny bit from 1937 to 1971, when it ceased to be legal tender.
 British One Pound Coin to be introduced in 2017.
 Australian 50cent coin
 Fijian 50 cents
 Tongan 50seniti, since 1974
 Solomon Islands 50 cents
 Croatian 25 kuna
 Romanian 5000 lei, 2001–2005
 Canadian penny, 1982–1996
 South Vietnamese 25 đồng, 1968–1975
 Zambian 50 ngwee, 1969–1992
 Malawian 50 tambala, 1986–1995
 Mexican 20 centavos, since 1992
 Teselation
 Four Examples
 Construction
 Use a compass to draw a circle
 Draw a pair of perpendicular lines that meet at the center of the circle. One horizontal and one verticle.
 Make two circle that center at the two spots where the verticle line intersects the circle. The curve of the two circles have to meet at the center of the original circle.
 Make two circle that center at the two spots where the horizontal line intersects the circle. The curve of the two circles have to meet at the center of the circle you made in step one.
 Starting at the top of the circle, where the verticle line meets the curve, draw a line from there to the nearest point where the large circle's curve intersects with a line or another curve.
 Draw another line from there to the the next intersection along the curve and keep on doing that in a clockwise(or counterclockwise) direction.
 Erase all lines and curves except the ones made in the past 2 steps.
 Graphing
 If a regular dodecagram with each side having 2 units long was graphed with the center at (0,0), the coordinate would be:
 If a regular dodecagram with each side having 2 units long was graphed with the center at (0,0), the coordinate would be:
 NonEuclidean Geometry
 Dodecagonal Antiprism
 See Also
