  An aperiodic prototile is a shape for which infinitely many copies can be
arranged to fill Euclidean space completely with no overlaps, but not in a
periodic pattern. Tiling theorists refer to such a prototile as an "einstein"
(a German pun on "one stone"). The possible existence of an einstein has been
pondered ever since Berger's discovery of large set of prototiles that in
combination can tile the plane only in a nonperiodic way. In this article we
review and clarify some features of a prototile we recently introduced that is
an einstein according to a reasonable definition. [This abstract does not
appear in the published article.]
