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Regular dodecagram
Regular star polygon 12-5.svg
A regular dodecagram
Type Regular star polygon
Edges and vertices 12
Schläfli symbol {12/5}
Coxeter diagram CDel node 1.pngCDel 12.pngCDel rat.pngCDel d5.pngCDel node.png
CDel node 1.pngCDel 6.pngCDel rat.pngCDel d5.pngCDel node 1.png
Symmetry group Dihedral (D12)
Internal angle (degrees) 30°
Dual polygon self
Properties star, cyclic, equilateral, isogonal, isotoxal

A dodecagram is a star polygon that has 12 vertices. There is one regular form: {12/5}. A regular dodecagram has the same vertex arrangement as a regular dodecagon, which may be regarded as {12/1}.

The name "dodecagram" combines the numeral prefix dodeca- with the Greek suffix -gram. The -gram suffix derives from ? (gramm?s), which denotes a line.[1]

Isogonal variations

A regular dodecagram can be seen as a quasitruncated hexagon, t{6/5}={12/5}. Other isogonal (vertex-transitive) variations with equally spaced vertices can be constructed with two edge lengths.

Regular polygon truncation 6 1.svg
Regular polygon truncation 6 2.svg Regular polygon truncation 6 3.svg Regular polygon truncation 6 4.svg

Dodecagrams as compounds

There are four regular dodecagram star figures: {12/2}=2{6}, {12/3}=3{4}, {12/4}=4{3}, and {12/6}=6{2}. The first is a compound of two hexagons, the second is a compound of three squares, the third is a compound of four triangles, and the fourth is a compound of six straight-sided digons. The last two can be considered compounds of two hexagrams and the last as three tetragrams.

Regular star figure 2(6,1).svg
Regular star figure 3(4,1).svg
Regular star figure 4(3,1).svg
Regular star figure 6(2,1).svg

Complete graph

Superimposing all the dodecagons and dodecagrams on each other - including the degenerate compound of six digons (line segments), {12/6} - produces the complete graph K12.

11-simplex graph.svg

Regular dodecagrams in polyhedra

Dodecagrams can also be incorporated into uniform polyhedra. Below are the three prismatic uniform polyhedra containing regular dodecagrams.

See also


  1. ^ , Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.



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