| It all depends on what paths you're allowed. In 2D, the brick is only a surface, although the surface may intersect the brick at any angle, and thus be triangular, quadri-, penta- or hexalateral, and may contain interior points and surface (boundary) points of the brick, or surface points only. In 3D, the brick has a definite "inside", but it is not reachable without deforming the surface of the brick, whether one breaks the brick, cuts it, drills a hole in it, what-have-you; every path that contains an interior point of the brick must intersect at least one of the brick's surfaces (for these purposes, a path that is contained entirely within the brick is not allowed, as there is no way in 3D to start movement within the brick's boundary). In 4 and more dimensions, one can plot paths that will intersect interior points of the brick without intersecting any of the brick's surfaces. |
