EDGE: the shape of dark matter haloes in the faintest galaxies

Collisionless dark matter only (DMO) structure formation simulations predict that dark matter (DM) haloes are prolate in their centres and triaxial towards their outskirts. The addition of gas condensation transforms the central DM shape to be rounder and more oblate. It is not clear, however, whether such shape transformations occur in 'ultra-faint' dwarfs, which have extremely low baryon fractions. We present the first study of the shape and velocity anisotropy of ultra-faint dwarf galaxies that have gas mass fractions of f(gas)(r < R-half) < 0.06. These dwarfs are drawn from the Engineering Dwarfs at Galaxy formation's Edge (EDGE) project, using high-resolution simulations that allow us to resolve DM halo shapes within the half-light radius (similar to 100pc). We show that gas-poor ultra-faints (M-200c <= 1.5 x 10(9)M(circle dot); f(gas) < 10(-5)) retain their pristine prolate DM halo shape even when gas, star formation, and feedback are included. This could provide a new and robust test of DM models. By contrast, gas-rich ultra-faints (M-200c > 3 x 10(9)M(circle dot); f(gas) > 10(-4)) become rounder and more oblate within similar to 10 half-light radii. Finally, we find that most of our simulated dwarfs have significant radial velocity anisotropy that rises to (beta) over tilde at R greater than or similar to 3R(half). The one exception is a dwarf that forms a rotating gas/stellar disc because of a planar, major merger. Such strong anisotropy should be taken into account when building mass models of gas-poor ultra-faints.