Here is a rolling octahedron version of the Nauru graph.
Each triangle side connects to the orientation the octahedron corresponding to rolling over that edge.
The F120B cubic symmetric graph can be obtained by rolling an icosahedron with 12 labelled faces.
In the version above the triangles overlap. Can someone make a version of F120B with 120 triangles? Ideally, almost all of the triangles would have a direct edge connection to two other triangles. The girth of F120B is 10, corresponding to rolling the icosahedron on the middle band of 10 triangles.
Perhaps one of these might work. I don't know an easy way to check.
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