[Freudenthal's magic square][1] of Lie algebras<br>
and the corresponding square of projective planes:

&#8477;P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
&#8450;P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
&#8461;P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
&#8576;P<sup>2</sup>

&#8450;P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
(&#8450;&otimes;&#8450;)P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;
(&#8450;&otimes;&#8461;)P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;
(&#8450;&otimes;&#8576;)P<sup>2</sup>

&#8461;P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
(&#8461;&otimes;&#8450;)P<sup>2</sup>&nbsp;&nbsp;&nbsp;
(&#8461;&otimes;&#8461;)P<sup>2</sup>$&nbsp;&nbsp;&nbsp;
(&#8461;&otimes;&#8576;)P<sup>2</sup>

&#8576;P<sup>2</sup>&nbsp;&nbsp;&nbsp;&nbsp;
(&#8576;&otimes;&#8450;)P<sup>2</sup>&nbsp;&nbsp;&nbsp;
(&#8576;&otimes;&#8461;)P<sup>2</sup>&nbsp;&nbsp;&nbsp;
(&#8576;&otimes;&#8576;)P<sup>2</sup>


<i>Also:</i> have a look at [John Baez's cheat sheet][2],<br>
and at the subsections <i>[G][3]</i><sub>2</sub>, <i>[F][4]</i><sub>4</sub>, <i>[E][5]</i><sub>6</sub>, <i>[E][6]</i><sub>7</sub>, <i>[E][7]</i><sub>8</sub>. 


  [1]: http://en.wikipedia.org/wiki/Freudenthal_magic_square
  [2]: http://math.ucr.edu/home/baez/octonions/node13.html
  [3]: http://math.ucr.edu/home/baez/octonions/node14.html
  [4]: http://math.ucr.edu/home/baez/octonions/node15.html
  [5]: http://math.ucr.edu/home/baez/octonions/node17.html
  [6]: http://math.ucr.edu/home/baez/octonions/node18.html
  [7]: http://math.ucr.edu/home/baez/octonions/node19.html