Dodecagram
A dodecagram is a star polygon that has 12 vertices. There is one regular form:. A regular dodecagram has the same vertex arrangement as a regular dodecagon, which may be regarded as.
The name "dodecagram" combines the numeral prefix ' with the Greek suffix '. The -gram suffix derives from γραμμῆς, which denotes a line.
Isogonal variations
A regular dodecagram can be seen as a quasitruncated hexagon, t=. Other isogonal variations with equally spaced vertices can be constructed with two edge lengths.Dodecagrams as compounds
There are four regular dodecagram star figures: =2, =3, =4, and =6. 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 straight-sided digons. The last two can be considered compounds of two hexagrams and the last as three tetragrams.2 | 3 | 4 | 6 |
Complete graph
Superimposing all the dodecagons and dodecagrams on each other – including the degenerate compound of six digons, – produces the complete graph K12.| black: the twelve corner points red: regular dodecagon green: =2 two hexagons blue: =3 three squares cyan: =4 four triangles magenta: regular dodecagram yellow: =6 six digons |
Regular dodecagrams in polyhedra
Dodecagrams can also be incorporated into uniform polyhedra. Below are the three prismatic uniform polyhedra containing regular dodecagrams.Dodecagrams can also be incorporated into star tessellations of the Euclidean plane.
Dodecagram Symbolism
Dodecagrams or twelve-pointed stars have been used as symbols for the following:*
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