This knot has no obvious symmetries. In the starting knot below, there are three pentagonal holes in which smaller versions of the knot could be placed. This was found to create a link rather than a knot, however (it wasn't unicursal), while using two copies as shown does result in a knot.
One possible starting self-similar knot:
After one iteration:
After two iterations:
All images copyright Robert Fathauer
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