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Regular dodecagram  

A regular dodecagram  
Type  Regular 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 
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Regular dodecagram  

A regular dodecagram  
Type  Regular 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 
A dodecagram is a star polygon that has twelve 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}.
Dodecagrams can also be incorporated into polyhedra. Below are the three prismatic uniform polyhedra containing dodecagrams.
There are 3 regular dodecagram star figures, {12/2} (2{6}), {12/3} (3{4}) and {12/4} (4{3}). The first is a compound of two hexagons, the second is a compound of three squares and the last is a compound of four triangles.
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}.
