نجمة إثنى عشرية

Regular dodecagram
Regular star polygon 12-5.svg
dodecagram منتظم
النوعمضلع نجمي منتظم
الأضلاع والرؤوس{{{p12/5-جوانب}}}
رمز شلفلي{{{{p12/5-شلفلي}}}}
مخططات كوكستر-دنكنCDel node 1.pngCDel 12.pngCDel rat.pngCDel d5.pngCDel node.png
CDel node 1.pngCDel 6.pngCDel rat.pngCDel d5.pngCDel node 1.png
مجموعة التماثلثنائي الأسطح (D{{{p12/5-جوانب}}})
الزاوية الداخلية (الدرجات){{{زاوية p12/5}}}°
الخصائصنجمي، دائري، متساوي الأضلاع، متوازي، متجانس الأضلاع

النجمة الإثنى عشرية dodecagram[1]، هي مضلع نجمي أو مركّب له إثنا عشر رأساً. There is one regular dodecagram polygon (with Schläfli symbol {12/5} and a turning number of 5). There are also 4 regular compounds {12/2}, {12/3}, {12/4}, and {12/6}.

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النجمة الإثناعشرية المنتظمة

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}.


النجوم الإثناعشرية كمركّبات منتظمة

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 straight-sided digons. The last two can be considered compounds of two compound hexagrams and the last as three compound tetragrams.

النجوم الإثناعشرية 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
الكثافة 1 2 3 4 5
Image Isotoxal hexagram.svg
{(6)α}
Concave isotoxal hexagon compound2.svg
2{3α}
Isotoxal rhombus compound3.svg
3{2α}
Intersecting isotoxal hexagon compound2.svg
2{(3/2)α}
Intersecting isotoxal dodecagon.svg
{(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.

Regular polygon truncation 6 1.svg
t{6}
Regular polygon truncation 6 2.svg Regular polygon truncation 6 3.svg Regular polygon truncation 6 4.svg
t{6/5}={12/5}

المخطط الكامل

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
K12 coloured.svg 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

النجوم الإثناعشرية كعديدات الأوجه

Dodecagrams can also be incorporated into uniform polyhedra. Below are the three prismatic uniform polyhedra containing regular dodecagrams (there are no other dodecagram-containing uniform polyhedra).

Dodecagrams can also be incorporated into star tessellations of the Euclidean plane.

رمزية النجمة الإثناعشرية

The twelve-pointed star is a prominent feature on the ancient Vietnamese Dong Son drums

Dodecagrams or twelve-pointed stars have been used as symbols for the following:

انظر أيضاً


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المراجع

  1. ^ γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus