How to make a mesh (having vectors perpendicular to the surface in various direction) thicker?

Thank you very much for this usefull information @SamPage. The offset is not working as the vectors are going in both inside and outside the oursin, meaning that at each point of the ursin the thickness is going to be added in different direction resulting in :
image

the dupmeshholeboundary is not working, rhino error: Edge must be on boundary of mesh. I also cant make it work the dupmeshedges command :(. I am still new to rhino so I am sorry for all my mistake.

My mesh hole is looking like this:

image