Star SVG is a certain kind of flat, nonconvex polygons, however, having no unambiguous mathematical definition.

## Star SVG First definition

The correct geometrical star could be the figure entered into the equilateral polygon constructed in the circle of any radius so that tops of a polygon coincided with tops of a star. Correct stars can be constructed with number of the parties not less than five. All stars constructed in polygons with number of sides 5 and more are characterised by certain ratio of the angle between adjacent tops to the corner of tops expressed by two whole numbers, depending on parity of number of sides of an initial polygon. If the number of sides of the initial polygon is even, the ratio of these angles is equal to 2 (two), that is, the angle between the neighboring vertices is twice as large as the angle of the vertices of the stars with the number of vertices 6 or more. If the number of sides of the initial polygon is odd, the ratio of the angle between the neighboring vertices to the angle of the vertices of the stars is 3 (three). For example, the angle between adjacent vertices of a five-pointed star (odd number of sides of the initial polygon) is 108°, and the angle of the vertex itself is 36°. The ratio 108 to 36 is equal to three. The angle between the neighboring vertices of the ten-pointed star (even number of the initial polygon) is 72°, and the angle of the vertex itself is 36°, i.e. the ratio 72 to 36 is 2 (two). It is interesting to note that the eight-pointed (octagonal) star constructed by turning one of the two superimposed squares by 45 degrees around the common center has the ratio of angles 1.5 (one and a half), i.e. the angle between the tops is 135°, and the angle of the top is 90°. Apparently, this 8-top star cannot be carried to the category of correct geometrical stars. The eight-pointed star with the usual ratio of these angles (2) has the angle between tops 90°, and the angle of the top is 45°. From each correct geometrical star it is possible to allocate the quadrilateral figure with three tops in the form of a peak having two pairs of sides of different length and three tops with identical value of a corner. For example, the mentioned five-pin star m.b. is formed by two peaks, the angle of vertices of which is equal to 36°, and one of the three vertices of each peak is combined with one of the vertices of the other peak. Therefore, by superimposing the vertices of each peak, you get a star with five vertices. Use of an equilateral triangle and a square for construction of correct 3-point and 4-point stars in the described way is not possible. For construction of these stars it is possible to use accordingly equilateral hexagon and octagon. Thus it is possible to construct any number of three- and four-pointed stars, but any of them will not correspond to the given parities of angles. Thus, correct geometrical stars could be recognized as pointed polygons with angles less than 90° at which the ratio of corners of tops to corners between adjacent tops is equal to two or three. Thus, the basic feature of a correct star is presence not less than two peaks in the form of four-sided figures with three equal corners which are in 2 or 3 times less than the external corner formed by the parties of next corners.

## Star SVG Second definition

Each vertex of a regular n-multiangle will be connected to m-na on a circle clockwise from it. The star obtained in this way is denoted as {n/m}. The intersection points of the sides are not considered as vertices. Such a star has n vertices and n sides, as well as a regular n-gon. It is also called a star polygon, and it is a star form of the corresponding n-gon.

The ratio of radii of 2 circles of a correct star with the above-stated variant of construction: external (on which there are tops of angles of star beams) and internal (on which there are points of intersection of the sides of neighboring beams).