  Consider the ten-dimensional spinor variety in the projectivization of a
half-spin representation of dimension sixteen. The intersection X of two
general translates of this variety is a smooth Calabi-Yau fivefold, as well as
the intersection Y of their projective duals. We prove that although X and Y
are not birationally equivalent, they are derived equivalent and L-equivalent
in the sense of Kuznetsov and Shinder.
