  We have established precise planet radii, semimajor axes, incident stellar
fluxes, and stellar masses for 909 planets in 355 multi-planet systems
discovered by Kepler. In this sample, we find that planets within a single
multi-planet system have correlated sizes: each planet is more likely to be the
size of its neighbor than a size drawn at random from the distribution of
observed planet sizes. In systems with three or more planets, the planets tend
to have a regular spacing: the orbital period ratios of adjacent pairs of
planets are correlated. Furthermore, the orbital period ratios are smaller in
systems with smaller planets, suggesting that the patterns in planet sizes and
spacing are linked through formation and/or subsequent orbital dynamics. Yet,
we find that essentially no planets have orbital period ratios smaller than
$1.2$, regardless of planet size. Using empirical mass-radius relationships, we
estimate the mutual Hill separations of planet pairs. We find that $93\%$ of
the planet pairs are at least 10 mutual Hill radii apart, and that a spacing of
$\sim20$ mutual Hill radii is most common. We also find that when comparing
planet sizes, the outer planet is larger in $65 \pm 0.4\%$ of cases, and the
typical ratio of the outer to inner planet size is positively correlated with
the temperature difference between the planets. This could be the result of
photo-evaporation.
