  We investigate the ground state of the spin $S=1/2$ Heisenberg
anti-ferromagnet on the Shuriken lattice, also in the presence of an external
magnetic field. To this end, we employ two-dimensional tensor network
techniques based on infinite projected entangled pair and simplex states
considering states with different sizes of the unit cells. We show that a
valence bond crystal with resonances over length six loops emerges as the
ground state (at any given finite bond dimension) yielding the lowest reported
estimate of the ground state energy $E_0/J = -0.4410 \pm 0.0001$ for this
model, estimated in the thermodynamic limit. We also study the model in the
presence of an external magnetic field and find the emergence of $0$, $1/3$ and
$2/3$ magnetization plateaus with states respecting translation and point group
symmetries that feature loop-four plaquette resonances instead.
