$X^1$, $X^2$, $X^1 X^2$
$Y^2$, $Y^1$, $Y^1 Y^2$
$X^1 Y^2$, $X^2 Y^1$, $Z^1 Z^2$
corresponding to two qubits in three directions, which is related to the 2-direction three qubit Mermin pentagram of the form The number theoretic nature of these objects is discussed in the arxiv link. M theorists will notice the likeness of the magic square to certain mixing matrices in HEP phenomenology.