  We introduce an $n$-dimensional analogue of the construction of tessellated
surfaces from finite groups first described by Herman and Pakianathan. Our
construction is functorial and associates to each $n$-ary alternating
quasigroup both a smooth, flat Riemannian $n$-manifold which we dub the open
serenation of the quasigroup in question, as well as a topological $n$-manifold
(the serenation of the quasigroup) which is a subspace of the metric completion
of the open serenation. We prove that every connected orientable smooth
manifold is serene, in the sense that each such manifold is a component of the
serenation of some quasigroup. We prove some basic results about the variety of
alternating $n$-quasigroups and note connections between our construction,
Latin hypercubes, and Johnson graphs.
