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Solutions for Act I Scene 4 - Polarity

Each picture looks somewhat like a 360 degree panorama view, as the left and right edges seem to match up. The title confirms this by referencing polar coordinates. In fact, this is a chessboard, viewed from eight different empty squares.

First construct the regions neighbouring to each view point, then combine them by matching piece colours, square colours and the edges of the board. The following board is reconstructed:

This is a Reversi game. The empty squares suggest that you should complete the game, by placing pieces in the order given by the pictures. The parity of the current game state, as well as the lack of legal white moves on the first empty square, implies it is black's turn. We obtain the following after completing the game:

The name of this symmetric symbol is taijitu, commonly used to represent the concept of yin and yang.

The answer is: taijitu