DESCRIPTION 
This exercise by Daniel Piker displays a few powerful geometry concepts using mesh geometry. Starting from a generic triangulated mesh, it uses the Mesh Dual command and tools developed by weaverbird to create a smoothened hexagonal variant.  

PROCEDURE   

1. Generic triangulated mesh
2. For each vertex, Mesh Dual connects the centers of its adjoining faces with closed polylines
3. These polylines are scaled down towards their centre  
4. The original and scaled curves are exploded and their start and end points are ordered on clearly separated on different data paths  
5. From this list of sub-lists with 4 points, quad faces are created  
6. These quads are joined into one closed mesh  
7. This mesh is thickened and then smoothened using a Catmull-Clark Subdivision