Is there a unicursal octagram? Tl;dr
Is there such a thing as a unicursal octagram?
Long question
The unicursal hexagram is the figure formed when you link all six vertices of a regular hexagon using a single continuous trace, rather than a set of overlaid triangles. Here is what it looks like:

It even have some occult meanings and other nice symbolism.
For reasons of arbitrary RPG system symmetries, I would like to know whether anyone has ever heard of a unicursal octagram, that is, the figure formed when you trace all the vertices of a regular octagon with a single trace. The rules are:

*

*The trace has a direction. That is, if the octagram is modelled as a graph, each vertex will have exactly one edge going towards it and exactly one edge going out of it.

*Crossings in the middle of the surrounding octagon are allowed, but more symmetric structures are preferred. Beauty is a goal.

I have googled it several times, but the word "unicursal" seem to be very tightly bound to the word "hexagram" in Google's mind, so the octagram's more famous brother is always stealing the spotlight, so my google searches weren't very successful.
Alternatively, I tried looking for questions here on MathSE about unicursal octagrams, but there weren't any. I figured I could ask one, then.

The reason for the "unicursal" in "unicursal hexagram" is because no other number $n$ of points prevents the existence of a nondegenerate regular star polygon on $n$ points. So unicursal octagrams, dodecagrams, etc. exist but they need not be qualified as such.

The number of nondegenerate $n$-point regular star polygons for $n\ge4$ is $\frac{\varphi(n)}2-1$, which is zero only for $n=4,6$.
