[seqfan] A301771 chordless cycles in the 3-Andrasfai graph

[Richard J. Mathar]

I cannot figure out why the number of chordless cycles
in the 3-Andrasfasi graph is A301771(3)=8.
My attempt so far is to plot the graph as in
https://www.mpia.de/~mathar/public/mathar20240225.pdf ,
cycles with green edges, edges of the graph not in the cycles
are dashed edges.

There is a chordless cycle of length 4 and a chordless
cycle of length 5 in it.

These two plots have been reduced such that cycles obtained
from these by rotations of 1/8th around the central axis
or flips are considered equivalent.
So the cycle of 4 has a multiplicity of 4 if all rotated
versions are included and the cycle of 5 has a multiplicity
of 8. (Flips not relevant here because both cycles have
a symmetry axis). So my assumption would be A301771(3)=4+8=12.
Am I missing something here?
[There is usually more than one Hamiltonian path 
that could serve as the "natural" rim in such planar figures.
Did I over-count something in using multiplicities
of 4 and 8 for the two different cycles?]
Am I supposed to ignore the cycles of length 4 because
they appear to be crossing in the planar drawing?

Best,
Richard