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    $\begingroup$ Haumea is fast rotating, Moon is tidally locked. Do you want to handwave tidal locking? $\endgroup$
    – Alexander
    Commented Jul 16, 2021 at 22:35
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    $\begingroup$ I already edited it. $\endgroup$
    – Xare
    Commented Jul 16, 2021 at 22:38
  • $\begingroup$ Well, it would look just like what you described - a triaxial ellipsoid, just as in the image. $\endgroup$ Commented Jul 17, 2021 at 16:51
  • $\begingroup$ A minor problem is that we scientifically can't have fast rotating icy body in place of our Moon. A sufficiently advanced civilization may be able to place it there, but it won't stay in its initial state for long. $\endgroup$
    – Alexander
    Commented Jul 17, 2021 at 18:47
  • $\begingroup$ @Alexander maybe if you put the new moon on a canted orbit around Earth then place a solar shade on a halo orbit at L1, could keep it cool enough. You could also give the orbit a precession of 1 year such that the shadow of the new moon (and the shadow of the shade) never fall on Earth. $\endgroup$
    – BMF
    Commented Jul 17, 2021 at 19:25