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The second embedded YouTube video is probably a reasonable explanation. The full tree is replaced with eight (maybe nine, actually?) billboards.

N, S, E, W, NE, SE, SW, NW, and one looking down from above. That's nine.

Ok, I have no idea, either.

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Those billboards are an alternative (the more traditional) impostor type. The octahedral impostors replace these billboards with a geodesic polyhedron of octahedral symmetry. Basically it subdivides the sides of an octahedron to approximate a sphere.

Not really. The octahedron defines the positions you pre-render the impostors from. The actual rendering uses a flat plane (like a regular billboard) but with a parallax shader and depth offset to make it look bent.

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