Hi Robert, As always, I enjoy the simplicity of your diagrams and it gives me a great opportunity to discover the story they are telling.
Like a map charts geographical features, geometry also tells a story because it is based on a reality. I look at the patterns based on similar attaching spheres. However, I am having difficulty in deciphering the reality on which the attached diagram is based.
The problem is with the hexagon, although symmetrical in one alignment I would not call it regular as it cannot be inscribed with a circle. As a result, when you try and construct a geometric dual, it is not possible.
Keep up the good work.
David
RobertLovesPi.net 
Nice!
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Thank you!
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Hi Robert, As always, I enjoy the simplicity of your diagrams and it gives me a great opportunity to discover the story they are telling.
Like a map charts geographical features, geometry also tells a story because it is based on a reality. I look at the patterns based on similar attaching spheres. However, I am having difficulty in deciphering the reality on which the attached diagram is based.
The problem is with the hexagon, although symmetrical in one alignment I would not call it regular as it cannot be inscribed with a circle. As a result, when you try and construct a geometric dual, it is not possible.
Keep up the good work.
David
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Yes, the hexagons are merely equilateral, not equiangular.
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