the supposed 15 hand holds is a little misleading as it doesn't account for holds where a hand is placed on the body, which is important to many dancing traditions, such as the mirror image polka hold, with the man's left arm stretched to his left holding his girl's right hand, and his right on her body, or the rotationally symmetric ceilidh hold, where both partners hold left hands, and pass their right hand over and through the hold to grasp their partner's left side, inside of their left arm. the statement needs a big caveat so it is clear that it does not accurately describe all real dance holds.
Yes all of that was purposefully left out. It's just about which hand is touching which other hand, not about how the hands are actually in contact. I was purposefully skipping those details to try and find something simple to build on.
