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seven

Why does following next->twin give vertices?

lizard

Would you ever want to give half-edges the ability to not be manifold? Eg maybe having twin be a list of halfedges for the star shape?

large_goobler

I'm also not certain why following a half-edge next to another half-edge twin would give a vertex. Or faces, or edges.

mateib

Why does following next->twin give vertices?

Following next->twin gives you a series of halfedges that orbit around the same vertex.

stroucki

Why is the hourglass figure not encodable, while if the faces were embedded in other parts of the mesh it would be ok? Don't the boundary faces enable this?