Problem #PRU-5279

Problem

Liam saw an unusual clock in the museum: the clock had no digits, and it’s not clear how the clock should be rotated. That is, we know that $1$ is the next digit clockwise from $12$, $2$ is the next digit clockwise from $1$, and so on. Moreover all the arrows (hour, minute, and second) have the same length, so it’s not clear which is which. What time does the clock show?