Simple Tiling

I did it at last! The first version of tiling from Simple Polygons that is fine (motif #8):

Well, these Simple Polygons are not the same as in my previous post. Here you can see red triangles, green squares and blue hexagons. If you want to tat polygon with N sides, you should tat N connected rings:
R X (picot or join to previous R) 3 - 3 - 3 - 3 (picot or join to next R) X
The question is, what does X equal to? In common case X is about 6 * ctg (pi / N).
So:

• for N = 3 X is about 4; 
• for N = 4 X is equal to 6; 
• for N = 6 X is about 10.

Well, I'm not absolutely sure about these numbers, I must say. I should try to tat such an example with some other thread, not Iris. Iris becomes not fine when you work with big rings. Rose is much better is this sense.
Anyway, the whole idea works! My first polygons were simple and pretty, but not functional, these are simple and functional, but not very pretty. I still believe that I can create some simple, pretty and functional pattern at the same time. Well, we'll see.

Experiments...

Last several days I was not very productive in tatting. Well, I tatted a lot but there is just nothing to show.
First of all, I tried another thread for my Hibiscus pattern, named Rose (I don't know why but a set of threads popular in Russia have floral names). On the photo it is left:

These "floral" threads do not have numbers. But if we calculate the thread number as length in meters per 1 gram, Iris is about #9 and Rose is about #7.
Hibiscus gave me a funny idea, that I have been trying to implement for last several days. There is a pretty thing in Math - tiling with regular polygons. I'm sure, that pictures here and here will explain this idea much better than any of my explanations. So, I decided to make very simple one-shuttle pattern that will present different regular polygons with slight modifications. Here is the first attempt (motif #7):

The pattern consists of all rings. If N is number of sides of polygon, you should tat N rings:
N (picot or join to the previous ring) 2 - 4 - 4 - 2 (picot or join to the next ring) N
The pattern is finished with lock join to the base of first ring.
Well, it seems to me, that these little motifs look fine. However, when I tried to connect such motifs into one of these tilings I couldn't! It took two unsuccessful attempts to understand that the length of one ring (e.g. 4 + 2 + 4 + 4 + 2 + 4 = 20 for square motif) doesn't equal to that one it should be (4 * 6 = 24), so the actual lengths of polygon's sides are different.
Now, when I know this, I work on another version of Simple Polygons, as I call them. Hopefully the third attempt will be better.