These complex tilings require either pair p,r to be from 2,2; 3,2; 3,3; 4,2; 4,4; 6,2; 6,3; 6,6; or one of their reversions.

The below also used values q follows the further requirement: 1/p + 2/q + 1/r = 1 each.

However, as long as p₁≠p₂ the used face would be isogonal-only and as long as r₁≠r₂ the used vertex figure would be isotoxal-only.

Incidence matrix according to Dynkin symbol

xp1-q1-or1   xp2-q2-or2   (N → ∞)

.     .     .     .   | p1p2N ♦    r1    r2 |  r1r2
--------------------+-------+------------+------
xp1   .     .     .   |    p1 | p2r1N     * |    r2
.     .     xp2   .   |    p2 |     * p1r2N |    r1
--------------------+-------+------------+------
xp1   .     xp2   .   ♦  p1p2 |    p2    p1 | r1r2N