  Time crystals appear when systems display a commensurate spontaneous breaking
of the discrete time translational invariance imposed by an external periodic
drive. No consensus on the definition has been reached as yet, but important
aspects comprise robustness against small variations of the parameters and the
initial quantum state. Often, disorder and interaction are thought to be
essential ingredients for the occurrence of time crystals. We study a
finite-length polarized XX spin chain engineered to display a spectrum of
equidistant energy levels without drive and show that it keeps a spectrum of
equidistant quasienergies in Floquet theory for a large variety of periodic
driving schemes. This interesting behavior is explained by mapping the XX spin
chain with $N+1$ sites to a single large spin with $S=N/2$ invoking the closure
of the group SU(2). For suitably tuned parameters this system realizes time
crystals of various periodicities for \emph{all} initial states. The robustness
against variations of the parameters is also discussed. Thereby, we establish a
clean system without interaction which can display the phenomenon of time
crystallization.
