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The many faces of fused cycles

Although many ring systems in molecules are quite easy to layout as 2D diagrams, there are some that are inherently 3D. Bridged rings are usually in this class; consider my favourite example molecule, cuneane:

Each of (A, B, C) is a particular layout of the same molecule, but with a different boundary (hexagon, pentagon, er...kind of fused squares). It would be nice to have a layout method that picked the same choice each time - regardless of the permutation of atoms and bonds. Even better if it could allow enumeration of the alternative possibilities.

As another example, consider a series based on twistane (which is a molecule) to two other graphs that may well not be actual molecules:

Twistane itself is in the middle, surrounded by five- and seven- ring equivalents. The upper layouts emphasise one ring in the graph while the lower ones emphasise the dual rings in each.


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