  The purpose of this short expository note is to provide an example exhibiting
some of the pathological properties of real-analytic subvarieties, where the
pathology can be visualized, and the proofs use only elementary properties of
analytic functions. We construct a compact irreducible real-analytic subvariety
$S$ of ${\mathbb R}^3$ of pure dimension two such that 1) the only a
real-analytic function is defined in a neighbourhood of $S$ and vanishing on
$S$ is the zero function, 2) the singular set of $S$ is not a subvariety of
$S$, nor is it contained in any one-dimensional subvariety of $S$, 3) the
variety $S$ contains a proper subvariety of dimension two. The example shows
how a badly behaved part of a subvariety can be hidden via a second
well-behaved component to create a subvariety of a larger set. The pathology is
visualized using several figures. Examples of these phenomena are known since
the time of Cartan, but hard to find in the English language literature.
