Comments
As can be seen, this particular creation process (‘drop’) gives one pentagon in all instances, no matter what unit and gradient is utilised. Generally the pentagons are asymmetrical, but also symmetrical with the ‘special case’. In the general sense, each pentagon has two angles of 90° of with three different side lengths, of 2, 2, 1 proportions for any given example. In the ‘special case’, the side lengths are of 3, 2 proportions. The pentagons are typically, but not necessarily ‘tall’. Of interest is that here are basically, topologically, of just two types. Of the two, obviously aesthetically better is the symmetrical pentagon, and furthermore it has the pleasing feature of the sides being of just two side lengths, rather than the three of the asymmetric pentagon. Aesthetically, the ‘extreme,’ extended examples are lacking, in that these are furthest away from an ‘average’ pentagon. The subsidiary hexagons are at right angles (which as I later show with other, different premises is not always so) which again is aesthetically pleasing. As can be seen, as a type, these examples with just the one pentagon are obviously more elegant than with two or more pentagons in the composition.

Variation

Tilings
As these are of the infinite type, of necessity I restrict the drawings to the first few gradient types. Broadly, a few suffice to show the general principle, and so a, for reasons of space saving further examples are not shown.

As can be seen, this procedure gives rise to two different pentagons. Although these are not symmetrical, they nonetheless give cause of interest. Perhaps of most note is that the subsidiary hexagons are now no longer par for all three sides; only one is. As can be seen, this slightly ‘weakens’ the premise of the typical Cairo-type (i.e. of subsidiary par hexagons), in that the tiles are no longer as aesthetic with all sides par hexagon, but instead are obviously more irregular. However, even with this weakened ‘feature’, they are still worthy in my opinion of the designator ‘Cairo-type’, and in any case are of interest in their own right. One interesting feature of these is the distribution of the pentagons, in that the like pentagons are ‘contiguous’, rather than at opposite ends of the subsidiary hexagon as occurs with other, non-related example
Of note is that this is yet another example of an ‘infinite’ type of composing, of which those shown is just a sample of the first few. As can be seen, the pentagons arising (and subsidiary hexagons) are the ‘same’ in all instances, from which one can extrapolate that all others must be of the same type.

Another Variation

Premise
This method retains the premise of stick crosses of the type as evinced by the above, but with the notable difference of both equal arm and asymmetrical arm crosses (previously, the study above was of like equal arm crosses, of 2 and 4 units), placed on the vertices of a square with a gradient (i.e. ‘drop’). Here, the stick crosses are placed as according to the orthogonals of the squared paper, with the premise of allowing the crosses to ‘drop’.

Tilings
As these are of the infinite type, of necessity I restrict the drawings to the first few gradient types. Broadly, a few suffice to show the general principle, and so for reasons of conciseness further examples are not shown.
Of note is that all the examples are based on a single type of unit size of cross, namely the 4, 4 and 4, 6. Obviously, this is, to say the least, inadequate, of which one could be accused of poor scientific practice, and with good reason for such a restricted sample. However, due to the time consuming nature of the diagrams, all drawn by hand, I curtail this, at least for know.

4 asymmetrical pentagons; 4, 4 and 4, 6 units, gradient 1:7, two subsidiary hexagons, one wholly par, the other just one side

4 asymmetrical pentagons; 4, 4 and 4, 6 units, gradient 1:8, two subsidiary hexagons, one wholly par, the other just one side

4 asymmetrical pentagons; 4, 4 and 4, 6 units, gradient 2:5, two subsidiary hexagons, one wholly par, the other just one side

4 asymmetrical pentagons; 4, 4 and 4, 6 units, gradient 2:6, two subsidiary hexagons, one wholly par, the other just one side

Comments

As can be seen, this procedure gives rise to generally four different pentagons, although three pentagons are to be found in a single ‘special case’ (which requires investigation at a later day). Although the four pentagons are not symmetrical, they nonetheless give cause of interest. Perhaps of most note is that the subsidiary hexagons are now no longer par for all three sides; only one is. As can be seen, this slightly ‘weakens’ the premise of the typical Cairo-type (i.e. of subsidiary par hexagons), in that the tiles are no longer as aesthetic with all sides par hexagon, but instead are obviously more irregular. However, even with this weakened ‘feature’, they are still worthy in my opinion of the designator ‘Cairo-type’, and in any case are of interest in their own right.
Of note is that this is yet another example of an ‘infinite’ type of composing, of which those shown is just a sample of the first few. As can be seen, the pentagons arising (and subsidiary hexagons) are the ‘same’ in all instances, from which one can extrapolate that all others must be of the same type i.e. topologically the same, with the exception of the ‘special case’.
Another aspect to this is one of interpretation, in that although the tilings were produced by stick crosses on a gradient, another interpretation of this is of par hexagons with subdivision, although this interpretation is open to scrutiny, in that the hexagons are not simply translated as regards the interior division, but rather translated and rotated.