  We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice
with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic
(FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and
thermodynamic properties. We show that the FM couplings do not sabotage the
magnetic disordering of the ground state due to the frustration from the AF
interactions inside each triangle, but trigger a fully gapped
inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with
emergent spin-1 degrees of freedom. We discover that with strengthening $J_e$,
the system scales exponentially, either with or without a magnetic field $h$:
the order parameter, the five critical fields that separate the $J_e$-$h$
ground-state phase diagram into six phases, and the excitation gap obtained by
low-temperature specific heat, all depend exponentially on $J_e$. We calculate
the temperature dependence of the specific heat, which can be directly compared
with future experiments.
