We construct simple triaxial generalisations of Navarro-Frenk-White haloes .
The models have elementary gravitational potentials , together with a density that is cusped like 1 / r at small radii and falls off like 1 / r ^ { 3 } at large radii .
The ellipticity varies with radius in a manner that can be tailored to the user ’ s specification .
The closed periodic orbits in the planes perpendicular to the short and long axes of the model are well-described by epicyclic theory , and can be used as building blocks for long-lived discs .

As an application , we carry out the simulations of thin discs of satellites in triaxial dark halo potentials .
This is motivated by the recent claims of an extended , thin disc of satellites around the M31 galaxy with a vertical rms scatter of \sim 12 kpc and a radial extent of \sim 300 kpc ( Ibata et al .
2013 ) .
We show that a thin satellite disc can persist over cosmological times if and only if it lies in the planes perpendicular to the long or short axis of a triaxial halo , or in the equatorial or polar planes of a spheroidal halo .
In any other orientation , then the disc thickness doubles on \sim 5 Gyr timescales and so must have been born with an implausibly small vertical scaleheight .