The following image has been in the news recently:
My understanding is that these are all the known (to-date) tilings of the plane using convex pentagons.
Can someone explain to me why the following are not in the list?
I don't have enough reputation here to comment, but I wanted to clarify Deusovi's answer.
The first tiling (Floret) is type 5, shown in the upper right of the diagram. The next tiling (Cairo) is type 4, shown in the middle of the diagram. The last tiling (Prismatic) is type 1, shown on the upper left of the diagram.
The first 1-13 types are sets of equations that each define an infinite number of valid pentagons. For the exact equations you may refer to http://www.mathpuzzle.com/tilepent.html.
Type 14 and Type 15 describe the pentagon angles exactly, allowing only for changes in scale.
They are - top right, middle, and top left. It's just that the ones in the diagrams use more "general" forms by not assuming any congruent sides or angles