Dodecagram

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Regular dodecagram
Star polygon 12-5.svg
A regular dodecagram
Type Regular polygon
Edges and vertices 12
Schläfli symbol {12/5}
t{6/5}
Coxeter diagram CDel node 1.pngCDel 12.pngCDel rat.pngCDel d5.pngCDel node.png
CDel node 1.pngCDel 6.pngCDel rat.pngCDel d5.pngCDel node 1.png
Symmetry group Dihedral (D12)
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 1 regular form: {12/5}.

All dodecagrams share the vertices of a dodecagon, which may be regarded as {12/1}.

Dodecagrams in polyhedra[edit]

Dodecagrams can also be incorporated into polyhedra. Below are the three prismatic uniform polyhedra containing dodecagrams.

Star figures[edit]

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.

Complete graph[edit]

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.

11-simplex graph.svg

See also[edit]

References[edit]