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A Poincar\'e-covariant quark+diquark Faddeev equation is used to developinsights into the structure of the four lightest$(I,J^P=\tfrac{3}{2},\tfrac{3}{2}^\pm)$ baryon multiplets. Whilst these systemscan contain isovector-axialvector and isovector-vector diquarks, one mayneglect the latter and still arrive at a reliable description. The$(\tfrac{3}{2},\tfrac{3}{2}^+)$ states are the simpler systems, with featuresthat bear some resemblance to quark model pictures, \emph{e.g}., their mostprominent rest-frame orbital angular momentum component is $\mathsf S$-wave andthe $\Delta(1600)\tfrac{3}{2}^+$ may reasonably be viewed as a radialexcitation 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 radialexcitation of the $\Delta(1700)\tfrac{3}{2}^-$; and whilst the rest-frame wavefunction of the latter is predominantly $\mathsf P$-wave, the leading piece inthe $\Delta(1940)\tfrac{3}{2}^-$ wave function is $\mathsf S$-wave, in conflictwith quark model expectations. Experiments that can test these predictions,such as large momentum transfer resonance electroexcitation, may shed light onthe nature of emergent hadron mass.

Composition of low-lying $\mathbf{J=\tfrac{3}{2}^\pm \,\Delta}$-baryons