P, D, and G topologies. In Section \[sec:results\] we present our results for both symmetric and non-symmetric stars, and we conclude in Section \[sec:summary\].

Strong Segregation Theory in general geometries {#sec:general}
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A single wedge {#sec:2a}
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We first recall some results for polymer brushes in strong segregation under melt conditions, and then show how to apply this to a general geometry. We consider a melt of star $A_{n_{\scriptscriptstyle
    A}}\!-\!B_{n_{\scriptscriptstyle B}}$ copolymers , comprising $n_{\scriptscriptstyle A}$ arms of *A*-blocks of mean square end-to-end distance $ R_{\scriptscriptstyle A}$ and similarly for the *B*-arms. The volume fraction $\phi$ of *A* material is [@mmnote] $$\phi = {n_{\scriptscriptstyle A} \Omega_{\scriptscriptstyle A}\over
\Omega},$$ where $\Omega=n_{\scriptscriptstyle A}\Omega_{\scriptscriptstyle
  A}+n_{\scriptscriptstyle B}\Omega_{\scriptscriptstyle B}$ is the total chain volume, and $\Omega_{\scriptscriptstyle A}$ and $\Omega_{\scriptscriptstyle B}$ are the volumes of single *A* and *B* arms. Our calculations are appropriate for strongly-segregated chains, for which interfaces are sharp on the scale of microphase lattice constants. In strong segregation the free energies of all microphases scale the same way with chain length and interfacial tension, so the phase boundaries become independent of the strength of the repulsion $\chi$ between *A* and *B* monomers.

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Consider an elementary wedge, as in Figure \[fig:wedge\], from 