Это всё складывала не я. Но разыскать это всё, выбрать, описать потребовало некоторого времени и усилий.
И получилась вот такая полная коллекция.
Это так называемые группы обоев (wallpaper groups) или двумерные кристаллографические группы. То есть, варианты симметрии, которые возможны в двумерных решётках. Их всего 17.
И под каждый удалось найти бумажный тесселеёшн (я всё ещё не знаю, как это по-русски).
Вот они, любуйтесь.
Цертус хочет, чтобы я всё это сложила. А я что, я ж разве против? ;)

Via Flickr:
Once looking at how I'm spreading pentagons on a sheet of paper, my husband asked me what I'm doing.
"I'm trying to make something like Penrose tiling" Being a mathematician, he said: "It's boring! You'd better make a collection of 17 plane crystallographic groups. I would be happy to have such a collection at home" Oh! He said something about my hobby which was not ironic! (Or... was it? No matter, it's too late...)
So... First, I should find out what are these plane crystallographic (or wallpaper) groups. There is an article in Wikipedia saying that "A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern", but it did not make the things clear for me.
Then I used the table from the article and classified all tessellations I've already made. And it appeared that almost half of them are already covered!
Then I went to Flickr to look for the rest... And here they are! Some of them are used very often, it was hard to choose only one example for each, but there are some very rarely used groups, I should look through all Origami Tessellations pool (over 9000 photos', literally!) to find a couple of examples.
The next step is to fold all of them...