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geometry[RegularStarPolygon] - define a regular star polygon
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Calling Sequence
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RegularStarPolygon(p, n, cen, rad )
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Parameters
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p
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the name of the regular star polygon
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n
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positive rational number > 2
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cen
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point which is the center of the n-gon
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rad
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number which is the radius of the circumscribed circle of the n-gon
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Description
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Let S be a rotation through angle  , and let A_0 be any point not on the axis of S. Then the points ![A[i]=(A[0])^((S)^(i)),i=...,-2,-1,0,1,2,...](/support/helpjp/helpview.aspx?si=5895/file04086/math80.png) are the vertices of a regular polygon n whose sides are the segments A_0A_1, A_1A_2, ...
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When n is an integer (greater than 2) this definition is equivalent to that given for regular polyhedra. But the polygon can be closed without n being integral; it is merely necessary that the period of S to be finite, i.e., that n be rational. We still stipulate that  since a positive rotation through an angle greater than Pi is the same as a negative rotation through an angle less than Pi.
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To access the information relating to a regular star polygon p, use the following function calls:
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form(p)
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returns the form of the geometric object
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(i.e., RegularStarPolygon2d if p is a regular polygon).
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DefinedAs(p)
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returns a list of vertices of p.
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sides(p)
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returns the side of p.
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center(p)
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returns the center of p.
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radius(p)
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returns the radius of the circum-circle of p.
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InteriorAngle(p)
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returns the interior angle of p.
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ExteriorAngle(p)
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returns the exterior angle of p.
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perimeter(p)
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returns the perimeter of p.
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area(p)
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returns the area of p.
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detail(p)
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returns a detailed description of the
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given regular polygon p.
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The command with(geometry,RegularStarPolygon) allows the use of the abbreviated form of this command.
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Download Help Document
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