The hyperplanes of the glued near hexagon Q(5,2) ⊗ Q(5,2)

With the aid of the computer algebra system GAP, we show that the glued near hexagon Q(5, 2) circle times Q(5, 2) has 16 isomorphism classes of hyperplanes. We give at least one explicit construction for a representative of each isomorphism class and we list several properties of such a representative

The hyperplanes of the U (4)(3) near hexagon

Combining theoretical arguments with calculations in the computer algebra package GAP, we are able to show that there are 27 isomorphism classes of hyperplanes in the near hexagon for the group U (4)(3). We give an explicit construction of a representative of each class and we list several combinatorial properties of such a representative