According to the wikipedia article on pentagonal tilings, the 14th type of pentagonal tiling is
completely determined, with no degrees of freedom
However, I was wondering why an affine stretch of the plane would (thus preserving the tiling) would not introduce a degree of freedom for the angles. If this affine stretch yields a subcase of a different type of pentagon, then this 14th case itself would be a subcase. Thus my question is:
Why is the 14th convex pentagon tiling uniquely determined, and not able to be stretched with an affine transformation to give it a degree of freedom?