I received two interesting replies from Christopher Klerk, @Factotum . If Iām understanding correctly, in the second tweet Christopher is saying that he believes that touching inside, contained, contained is an additional configuration.

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Thanks @apm - and an indirect "Hello!" to Christopher, if he continues to read this thread! :)

Christopher is correct pointing out at least one missing configuration, and I already found another one. The problem here really is that the asymmetrical interactions ("touching inside" and "contained") can lead to multiple variants being possible where I only considered one to exist.

This can happen if there (a) is more than one asymmetrical interaction, and (b) the remaining symmetrical interactions aren't all the same.

In many cases, it looks as if the variants aren't possible to draw - for example "A contains B, B contains C, C touches A on the inside" is a theoretical third variant of the alternative solution Christopher found, but one that's just impossible. Still, there are many potential configurations that still need to be checked.

(This, by the way, throws the whole "Tetrahedral numbers" tangent out of the window. ;))