Why can’t a tetragram exist
In: 1
Depending on your definition, they can exist. One definition of polygram is the general case into which all polygons and some non-polygons fall into.
But I’m assuming you mean certain types of star polygons, like the traditional pentagram star. Polygrams are usually described by their [Schlafli symbol](https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol#Regular_polygons_(plane)), which for a pentagon is {5} and for a standard pentagram is {5/2}.
What would a four-sided polygram look like? If it’s {4/1} or {4/3}, you just get a quadrilateral. If it’s {4/2}, you have two pairs of vertices, connected by crossing line segments. If it’s {4/4}, you have four unconnected vertices, each alone in space. To get something interesting in the Schlafli notation, your second number has to be greater than or equal to 2, less than vertices – 1, and relatively prime to the number of vertices. When vertices = 4, there is no integer that has that property.
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