  We report that four properties of cuprates and their evolution with doping
are consequences of simply counting four-site plaquettes arising from doping:
(1) the universal Tc phase diagram (superconductivity between \approx0.05 and
\approx0.27 doping per CuO2 plane, and optimal Tc at \approx0.16), (2) the
universal doping dependence of the room-temperature thermopower, (3) the
superconducting neutron spin resonance peak (the "41 meV peak"), and (4) the
dispersionless scanning tunneling conductance incommensurability. Properties
(1), (3), and (4) are explained with no adjustable parameters, and (2) is
explained with exactly one. The successful quantitative interpretation of four
very distinct aspects of cuprate phenomenology by a simple counting rule
provides strong evidence for four-site plaquette percolation in these
materials. This suggests that inhomogeneity, percolation, and plaquettes play
an essential role in cuprates. This geometric analysis may provide a useful
guide to search for new compositions and structures with improved
superconducting properties.

Superconductivity;Strongly Correlated Electrons