Dodecagram

Regular dodecagram
Regular dodecagram
	cyclic, equilateral, isogonal, isotoxal
Dual polygon	self

In

turning number

of 5). There are also 4 regular compounds

{12/2},

{12/3},

{12/4},

and

{12/6}.

Regular dodecagram

There is one regular form: {12/5}, containing 12 vertices, with a

turning number of 5. A regular dodecagram has the same vertex arrangement as a regular dodecagon

, which may be regarded as {12/1}.

Dodecagrams as regular compounds

There are four regular dodecagram

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 compound hexagrams

and the last as three compound tetragrams.

2{6}
3{4}
4{3}
6{2}

Dodecagrams as isotoxal figures

An

isotoxal polygon

has two vertices and one edge type within its symmetry class. There are 5 isotoxal dodecagram star with a degree of freedom of angles, which alternates vertices at two radii, one simple, 3 compounds, and 1 unicursal star.

Isotoxal dodecagrams
Type	Simple	Compounds			Star
Density	1	2	3	4	5
Image	{(6)_α}	2{3_α}	3{2_α}	2{(3/2)_α}	{(6/5)_α}

Dodecagrams as isogonal figures

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.

t{6}			t{6/5}={12/5}

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.

K₁₂
	black: the twelve corner points (nodes) red: {12} regular dodecagon green: {12/2}=2{6} two hexagons blue: {12/3}=3{4} three squares cyan: {12/4}=4{3} four triangles magenta: {12/5} regular dodecagram yellow: {12/6}=6{2} six digons