  Delta ($\delta$)-spots are active regions (ARs) in which positive and
negative umbrae share a penumbra. They are known to be the source of strong
flares. We introduce a new quantity, the degree of $\delta$ (Do$\delta$), to
measure the fraction of umbral flux participating in the $\delta$-configuration
and to isolate the dynamics of the magnetic knot, i.e. adjacent umbrae in the
$\delta$-configuration. Using Helioseismic and Magnetic Imager data, we analyze
19 $\delta$-spots and 11 $\beta$-spots in detail, and 120 $\delta$-spots in
less detail. We find that $\delta$-regions are not in a $\delta$-configuration
for the entire time but spend 55$\%$ of their observed time as $\delta$-spots
with an average, maximum Do$\delta$ of 72$\%$. Compared to $\beta$-spots,
$\delta$-spots have 2.6$\times$ the maximum umbral flux, 1.9$\times$ the flux
emergence rate, 2.6$\times$ the rotation, and 72$\times$ the flare energy. On
average, the magnetic knots rotate 17$^{\circ}$ day$^{-1}$ while the
$\beta$-spots rotate 2$^{\circ}$ day$^{-1}$. Approximately 72$\%$ of the
magnetic knots present anti-Hale or anti-Joy tilts, contrasting starkly with
only 9$\%$ of the $\beta$-spots. A positive correlation exists between
$\phi_{Do\delta}$ and the flare energy emitted by that region. The
$\delta$-spots obey the hemispheric current helicity rule 64$\%$ of the time.
84$\%$ of the $\delta$-spots are formed by single flux emergence events and
58$\%$ have a quadrupolar magnetic configuration. The $\delta$-spot
characteristics are consistent with the formation mechanism signatures as
follows: 42$\%$ with the kink instability or Sigma effect, 32$\%$ with
multi-segment buoyancy, 16$\%$ with collisions and two active regions that are
unclassified but consistent with a rising O-ring.
