The Banach–Mazur distance between $C([1,\omega ^n])$ and $C([1,\omega ])$

We give precise values of the Banach–Mazur distance between spaces $C([1,\omega ^n])$ and $C([1,\omega ])$ of all continuous real-valued functions on ordinal intervals endowed with the order topology. This solves a long-lasting problem posed by Bessaga and Pełczyński.