  Geometrically frustrated systems with a large degeneracy of low energy states
are of central interest in condensed-matter physics. The kagome net - a pattern
of corner-sharing triangular plaquettes - presents a particularly high degree
of frustration, reflected in the non-dispersive orbital bands. The ground state
of the kagome quantum antiferromagnet, proposed to be a quantum spin liquid or
valence bond solid, remains uncertain despite decades of work. Solid-state
kagome magnets suffer from significant magnetic disorder or anisotropy that
complicates the interpretation of experimental results. Here, we realize the
kagome geometry in a two-dimensional optical superlattice for ultracold
$^{87}$Rb atoms. We employ atom optics to characterize the lattice as it is
tuned between various geometries, including kagome, one-dimensional stripe, and
decorated triangular lattices, allowing for a sensitive control of frustration.
The lattices implemented in this work offer a near-ideal realization of a
paradigmatic model of many-body quantum physics.
