Let $E$ and $F$ be two Banach spaces. We say that their unit spheres are H\"{o}lder equivalent if there is a bijection $f$ between their unit spheres such that $f$ and $f^{-1}$ are H\"{o}lder continuous. In this talk, for a given $1<p<\infty$ we prove that all subspaces and quotient subspaces of $L_p[0,1]$ are equi-H\"{o}lder equivalent. In particular, the explicit H\"{o}lder constants and H\"{o}lder exponents will be provided.