File:Academ Stellated dodecagon.svg

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File:Academ Stellated dodecagon.svg - Wikipedia

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DescriptionAcadem Stellated dodecagon.svg	English: Extend every side of a given regular polygon can start a construction of another regular polygon, provided that the extensions intersect. Such a construction and its result are called a stellation of the initial polygon, if this polygon and the result are respectively convex and not convex. On the image is given a convex regular dodecagon. Twelve straight lines in black are extensions of its sides. Each black line cuts ten other black lines. Each intersection point is counted two times if we multiply ten by twelve, so there are sixty intersection points, including the vertices of the initial polygon. Among the sixty points, twelve points are the vertices of the polygon, the only one up to similarity, being regular and not convex and having twelve sides. To construct such a dodecagon from the given regular dodecagon, another way is to draw the segment joining A and B, and all the diagonals equal to this one. To construct the stellation, we choose a vertex of the given polygon as start point: point A, and then a rotation sense around the center of the polygon: anticlockwise on the image. In other words, we choose a ray (a half-line) with origin A, containing a side of the convex polygon. Running along this ray from point A, our pencil stops at the fifth intersection with a black line: point F, first vertex of the star. And then from point F, our pencil runs along the new black line up to a second vertex of the convex polygon: point B, start point of the second step. The process consists of twelve steps, repeated until we come back to point A, after passing through all the intersection points: 12 × 5 = 60 points. To draw attention on the intersection points of the first steps, there are two times five bicolour disks on the intersections. If an integer lower than 5 replaces 5 in the process, a convex regular polygon is constructed, not a stellation. Each side of the result contains a side of the initial polygon, of course. With 4 instead of 5, we construct an equilateral triangle. With 3 instead of 5 we get a square, with 2 a regular hexagon. We construct nothing but the initial polygon if we replace 5 with 1. In Schläfli's notation, where the first integer is the number of sides of the regular polygon, the results are denoted by {12;5} for the stellation, {3;1}, {4;1}, {6;1}, {12;1} for the other constructions.
Date	28 June 2012
Source	Own work
Author	Baelde
SVG development InfoField	The SVG code is valid. This /Baelde was created with a text editor.

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	Date/Time	Dimensions	User	Comment
current	07:37, 14 September 2012	750 × 750 (3 KB)	Baelde	the accent on two steps of the stellation, with five intersection points for each step
	07:57, 9 July 2012	600 × 600 (859 bytes)	Baelde	tighter margins
	21:32, 28 June 2012	625 × 625 (872 bytes)	Baelde	{{Information \|Description ={{en\|1=The twelve blue segments are the sides of a stellation of the convex dodecagon, the surface of which is in blue. Point ''T'' is the shared center of the regular dodecagons.}} \|Source ={{own}...

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Stellation

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Usage on ar.teknopedia.teknokrat.ac.id
- تمديد مضلع
Usage on es.teknopedia.teknokrat.ac.id
- Estelación
Usage on he.wikipedia.org
- כוכב (גאומטריה)
Usage on it.teknopedia.teknokrat.ac.id
- Stellazione
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- Stelare
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- Образование звёздчатой формы
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- Ззірчення

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