Dodecagram
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 combine a numeral prefix, dodeca, with the Greek suffix gram. The gram suffix derives from γραμμῆς (grammēs) meaning a line.^{[1]}
Isogonal variations
A regular dodecagram can be seen as a quasitruncated hexagon, t{6/5}={12/5}. Other isogonal (vertextransitive) variations with equal spaced vertices can be constructed with two edge lengths.
t{6} 
t{6/5}={12/5} 
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 straightsided digons.
2{6} 
3{4} 
4{3} 
6{2} 
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 K_{12}.
Regular dodecagrams in polyhedra
Dodecagrams can also be incorporated into uniform polyhedra. Below are the three prismatic uniform polyhedra containing regular dodecagrams.
See also
References
 Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0716711931.
 Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATOASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70.
 John H. Conway, Heidi Burgiel, Chaim GoodmanStrass, The Symmetries of Things 2008, ISBN 9781568812205 (Chapter 26. pp. 404: Regular starpolytopes Dimension 2)