  The superconducting circuit community has recently discovered the promising
potential of superinductors. These circuit elements have a characteristic
impedance exceeding the resistance quantum $R_\text{Q} \approx
6.45~\text{k}\Omega$ which leads to a suppression of ground state charge
fluctuations. Applications include the realization of hardware protected qubits
for fault tolerant quantum computing, improved coupling to small dipole moment
objects and defining a new quantum metrology standard for the ampere. In this
work we refute the widespread notion that superinductors can only be
implemented based on kinetic inductance, i.e. using disordered superconductors
or Josephson junction arrays. We present modeling, fabrication and
characterization of 104 planar aluminum coil resonators with a characteristic
impedance up to 30.9 $\text{k}\Omega$ at 5.6 GHz and a capacitance down to
$\leq1$ fF, with low-loss and a power handling reaching $10^8$ intra-cavity
photons. Geometric superinductors are free of uncontrolled tunneling events and
offer high reproducibility, linearity and the ability to couple magnetically -
properties that significantly broaden the scope of future quantum circuits.
