  We develop the spectroscopy of $c\bar c c\bar c$ and other all-heavy
tetraquark states in the dynamical diquark model. In the most minimal form of
the model (e.g., each diquark appears only in the color-triplet combination;
the non-orbital spin couplings connect only quarks within each diquark), the
spectroscopy is extremely simple. Namely, the $S$-wave multiplets contain
precisely 3 degenerate states ($0^{++}$, $1^{+-}$, $2^{++}$) and the 7 $P$-wave
states satisfy an equal-spacing rule when the tensor coupling is negligible.
When comparing numerically to the recent LHCb results, we find the best
interpretation is assigning $X(6900)$ to the $2S$ multiplet, while a lower
state suggested at about $6740$ MeV fits well with the members of the $1P$
multiplet. We also predict the location of other multiplets ($1S$, $1D$, etc.)
and discuss the significance of the $cc$ open-flavor threshold.
