Played around with this concept in coral draw. This should be a quick understanding of how tesselation works.
1. This is a vector copy I did of barry's first picture
2. I took it an made the same multiple copy
3. Then I rotated each one to a different side / angle. The arrows indicate which direction i turned
4. Here it is touching (its rough but you should get the idea) Creating a nice patterned layout
I hope this helps folks understand a little better