algorithmic modeling for Rhino
The mesh class in RhinoCommon is a face-vertex structure. These do not carry information about edges as such. If you need to query edge topology and traverse edges in general, the half-edge mesh structure is more appropriate. In Rhino/Grasshopper you can use the Plankton library by Daniel Piker and Will Pearson for this. I believe there are also other half-edge mesh plugins/libraries out there in Grasshopper land.
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