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Regular dodecagram  

A regular dodecagram  
Type  Regular star polygon 
Edges and vertices  12 
Schläfli symbol  {12/5} t{6/5} 
Coxeter diagram  
Symmetry group  Dihedral (D_{12}) 
Internal angle (degrees)  30° 
Dual polygon  self 
Properties  star, cyclic, equilateral, isogonal, isotoxal 
Star polygons 


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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 γραμμῆς (grammēs), which denotes a line.^{[1]}
A regular dodecagram can be seen as a quasitruncated hexagon, t{6/5}={12/5}. Other isogonal (vertextransitive) variations with equally spaced vertices can be constructed with two edge lengths.
t{6} 
t{6/5}={12/5} 
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 straightsided digons. The last two can be considered compounds of two hexagrams and the last as three tetragrams.
2{6} 
3{4} 
4{3} 
6{2} 
Superimposing all the dodecagons and dodecagrams on each other – including the degenerate compound of six digons (line segments), {12/6} – produces the complete graph K_{12}.
Dodecagrams can also be incorporated into uniform polyhedra. Below are the three prismatic uniform polyhedra containing regular dodecagrams (there are no other dodecagramcontaining uniform polyhedra).
Dodecagrams can also be incorporated into star tessellations of the Euclidean plane.