Let $S$ be a set in ${\mathbb{R}}^n$ and suppose that $S$ is triangulable. ($S$ is triangulable means that when regarded as a space, it has a triangulation.)

If there is a homeomorphism $h: {\mathbb{R}}^n \to {\mathbb{R}}^n$ such that $h(S)$ is a polyhedron, we say that $S$ is tamely imbedded.

If $S$ is triangulable but no such homeomorphism exists $S$ is said to be wild.

In ${\mathbb{R}}^2$ every 1-sphere is tamely imbedded. But in ${\mathbb{R}}^3$ there are wild arcs, 1-spheres and 2-spheres.