Not every symmetric hexagon is of this kind. A necessary and sufficient condition to be of this kind is that, placed with its center at (0,0) it has three consecutive vertices of the kind A', B', B'-A' (or A', B', A'+B').

HexagonsSymmetricRepeat.html

Poncelet.html

Symmetric_hexagons.html

Symmetric_hexagons_All.html

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