Dual Mesh with Mesh Face Offset

Simple and quick without images…

How do you achieve a Dual Mesh (Tri to Hex Mesh) and can offset the mesh face edges to inside, influenced by distance attractor?

Basically Cytosceleton, but instead of Edge Thickness, Offset Mesh Face, so that the thickened edges have same thickness from face to face.

I tried the to construct a mesh from Weaverbird’s Dual Graph, but it generates only non-coplanar lines, that I cant offset.

Many thanks,
Solomon

EDIT:

Two negative side effect of cyto is that the thickness also in mesh normal direction increases - I would need that to be the same to prevent use too much PMMA. Also the biggest holes get smaller and that should be the opposite or as said above controllable.

Basically I only need to get a TRI Mesh to a co-planar Hex Mesh - did the offset already.