This page uses content from Wikipedia and is licensed under CC BYSA.
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 
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.