Talk:Polygram (geometry)

Sources?

• [1] A polygram is like a polygon but the sides are allowed to cross. A polygram of n-sides or vertices is called an n-gram and for particular values of n we can give them individual names as for polygons. However there is no such thing as a 'trigram', since three successive line segments cannot cross anywhere; the first case is a tetragram, followed by pentagram, hexagram, heptagram, octagram, and so on.

  A regular polygram has all sides and angles equal. A tetragram cannot be regular, it can however be quasiregular, that is have the same vertices as a regular polygon; the first case of a regular polygram is the pentagram; there are also two quasiregular pentagrams. From six points we can derive eleven quasiregular hexagrams; none regular, one is asymmetric. The suffixes in the dagram indicate the numbers of different orientations in which each polygram can be seen if the points are fixed in place (thus 1 indicates regular).

• [2] A regular polygram {n/k} is generalization of a (regular) polygon on n sides (i.e., an n-gon) obtained by connecting every ith vertex around a circle with every (i+k)th, "picking up" the pencil as needed to repeat the procedure after traversing the circle until none of the vertices remain unconnected.
• [3] A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of distinct unicursal polygrams that can be formed from n points on circle with no two adjacent for n=1, 2, ... are 1, 0, 0, 0, 1, 3, 23, 177, 1553,