



 
Roger, As I interpret your question, what you want is a shell composed of hexagons attached along their edges. In such a case, what you probably want is not a tetrahedron (composed of 4 equilateral triangles), but a geodesic dome  this figure is based on the icosahedron. It will have 12 vertices symmetrically placed about the sphere at which 5 hexagons meet, and a large number of vertices where 6 hexagons come together. Details of their construction (including how many hexagons are possible) can be found on the internet. Chris  


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