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In Type Theory there is Rule: Every action is reversible.

There are 7 groups for 1d repeating pattern (Frieze groups).

  1. Group 1: only translations.
  2. Group 2: only glide reflection.

Why Cayley diagrams do not contain reversible action for these 2 groups? How can I get back to prev state? I suppose it is due to infinity...

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Some other groups contain reversible action:

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