An irregular* pentagon *means that the sides are not all the same length
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Cylinder
because you can't just change one of the angles or one of the side lengths without breaking the triangle. All the angles and sides re-inforce each other. Image a square made out of sticks that are attached loosely at the corners. You can squish two of the corners together to make a diamond shape, and you haven't changed the length of the sides. But if you have a triangle made out of sticks, you can't change it's shape without destroying it.
The most rigid shape that you can make out of straight pieces is the triangle.
triangle , square , rectangle
No. Hexagons and squares will each tessellate by themselves but one can not make a tessellation out of hexagons and squares combined. However, if you add in a third shape, the triangle, one can make a tessellation.