The original idea of Farinella et al. [1] that rubble pile asteroids can have figures of equilibrium, is rehabilitated. Albeit asteroids generally have a broad distribution of shapes and do not follow sequences of (hydrostatic) equilibrium, we show that some asteroids are indeed Jacobi or Darwin ellipsoids. Such statement is obtained from an analysis of their ellipsoidal shape (a:b:c) together with recent measures of their mass and bulk density [2,3]. This means that both their shape and adimensional rotation frequency sbond Omega =Omega /(pi rho G) follow sequences of equilibrium [4,5]. Jacobi and Darwin figures are obtained for uniformly rotating mass of (inviscid as well as compressible) fluids and relatively large angular momentum. Interestingly these objects appear to preferably be binaries. We moreover show that the porosity of such objects is relatively large (approx. 40%) indicating that they are loose rubble piles, yet with dense packing. Last we show that, given the observed bulk-densities, these bodies must be homogeneous bodies of uniform density distribution. Thus, though solid-solid friction must occur in such aggregates, the surface of these bodies is a surface of level similar to that of inviscid fluids. Comparison to other asteroids of similar mass either possessing a moonlet or with no known satellites should shed light on their formation history and/or constrains on collisional evolution. Binaries with low eccentricities and inclination (hence prograde orbit) should preferably be the outcome of catastrophic disruption as is supposed for members of dynamical family [6,7].