In the early 1970s Pelczynski noticed that the only surjective isometries on $C(K)$ for the following compact Hausdorff space $K$ are $pm Id$. I believe this was the first such example.
Quoting from Davis in “Separable Banach spaces with only trivial isometries”: Let $K$ be a dendrite containing for each $n>2$ exactly one cut-point of degree $n$ so that the cut-points are dense in $K$. Then the only surjective homomorphism of $K$ is the identity.” Banach-Stone then yields the result.
My question is: How does one construct $K$?
One of my issues is that I don’t know some of the basic definitions. What is the degree of a cut point? Googling has not been very helpful.