  This paper explores the birational geometry of a general Horrocks-Mumford
quintic threefold, describing the set of all minimal models up to marked
isomorphism, the movable fan (the way in which the nef cones of all these
models are arranged to form the movable cone), and the birational automorphism
group. There are infinitely many models up to marked isomorphism, falling into
just eight (unmarked-) isomorphism classes.
