# Circular Hand-holding

There are 6 people who are holding hands, such that each person is holding hands with exactly 2 other people. How many ways are there for them to do that?

Details and assumptions

Reflections count as distinct ways. Rotations count as the same way.

Each left hand grabs hold of a right hand.

A, B, C, D, E, F are arranged clockwise in a circle (with A at the 'top'), with A's left hand is holding on to B, so on and so forth. A reflection of this will be A, F, E, D, C, B are arranged clockwise in a circle (with A at the 'top'), with A's left hand holding on to F, so on and so forth. A rotation (of the first scenario) would be if C, D, E, F, A, B are arranged clockwise in a circle (with C at the 'top'), with C's left hand holding on to D, so on and so forth.

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