  The Fermi surface of a conventional two-dimensional electron gas is
equivalent to a circle, up to smooth deformations that preserve the orientation
of the equi-energy contour. Here we show that a Weyl semimetal confined to a
thin film with an in-plane magnetization and broken spatial inversion symmetry
can have a topologically distinct Fermi surface that is twisted into a
$\mbox{figure-8}$ $-$ opposite orientations are coupled at a crossing which is
protected up to an exponentially small gap. The twisted spectral response to a
perpendicular magnetic field $B$ is distinct from that of a deformed Fermi
circle, because the two lobes of a \mbox{figure-8} cyclotron orbit give
opposite contributions to the Aharonov-Bohm phase. The magnetic edge channels
come in two counterpropagating types, a wide channel of width $\beta
l_m^2\propto 1/B$ and a narrow channel of width $l_m\propto 1/\sqrt B$ (with
$l_m=\sqrt{\hbar/eB}$ the magnetic length and $\beta$ the momentum separation
of the Weyl points). Only one of the two is transmitted into a metallic
contact, providing unique magnetotransport signatures.
