  A Poincar\'e-covariant quark+diquark Faddeev equation is used to develop
insights into the structure of the four lightest
$(I,J^P=\tfrac{3}{2},\tfrac{3}{2}^\pm)$ baryon multiplets. Whilst these systems
can contain isovector-axialvector and isovector-vector diquarks, one may
neglect the latter and still arrive at a reliable description. The
$(\tfrac{3}{2},\tfrac{3}{2}^+)$ states are the simpler systems, with features
that bear some resemblance to quark model pictures, \emph{e.g}., their most
prominent rest-frame orbital angular momentum component is $\mathsf S$-wave and
the $\Delta(1600)\tfrac{3}{2}^+$ may reasonably be viewed as a radial
excitation of the $\Delta(1232)\tfrac{3}{2}^+$. The
$(\tfrac{3}{2},\tfrac{3}{2}^-)$ states are more complex: the
$\Delta(1940)\tfrac{3}{2}^-$ expresses little of the character of a radial
excitation of the $\Delta(1700)\tfrac{3}{2}^-$; and whilst the rest-frame wave
function of the latter is predominantly $\mathsf P$-wave, the leading piece in
the $\Delta(1940)\tfrac{3}{2}^-$ wave function is $\mathsf S$-wave, in conflict
with quark model expectations. Experiments that can test these predictions,
such as large momentum transfer resonance electroexcitation, may shed light on
the nature of emergent hadron mass.
