From surfaces to hollow tetrahedron

Hi all,

I've been struggling with this for some time. I would like to turn the model (bottom) into a hollow tetrahedron (top). I was thinking about offsetting the edges inward, deleting the "hole" then extruding the surfaces in the inwards along their normals. I'm just having trouble firstly offsetting the edges along the surfaces, and then extruding the joined surfaces inwards.

Thanks,

Laurens