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In the attached image how can I delete the 2 highlighted vertices and edge and leave the surrounding edges, faces intact?enter image description here

When I hit 'X' and select 'vertices', a gaping hole is created with adjoining faces/edges deleted.

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In Edge Select Mode, select the edge you want to get rid of, press the space bar and type dissolve... then choose dissolve edges.

enter image description here

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To remove an edge while keeping surrounding geometry, in Blender terminology you Dissolve it.

This can be done 2 ways:

  1. Press: Delete -> Dissolve Edges. or...
  2. Press: Ctrl-X
    (when you're in edge mode - since this is context-sensitive dissolve - which dissolves verts/edges/faces based on the current mode).
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