well, your sculptmap IS inside out...
So the face normals MUST be pointing in the wrong direction.
maybe two important rules about sculpties ... for clarification...
Rule 1: Sculpties are made out of planes. all of them, even the torus and the sphere.
Rule 2: Sculpties have only one side. The opposite side IS NOT RENDERED.
Now what does that mean... ? If you see the inside out effect, then you do not look at the rendered side of the object, but you look through the npot rendered side and see the rendered side from "behind". That makes the effect. A simple example (well not sooo simple): Take a plane plane. Look from one side at it. You see it is rendered (visible if you like better). Now go to the other side of the plane. Woooosh it's gone... No, its not rendered

Now think what happens when you bend this plane to a cylinder...
Now normals (face normals): think of such a normal as a stick, which is positioned on the face and points out perpendicular to the face itself. if the normal points towards your eye, the face is visible. If the normal points away from your eye, it is invisible.
Now think about what happens when you mirror along one axis or 3 axes...
In both cases the face normals are also mirrored. now... under some circumstances (which i do not understand to its fullness) the normals end up pointing in the wrong direction. If that happens... Inside out effect...
BTW you can VERY EASILY mirror a sculptie unintentionally when you use scale and move the mouse. Sometimes (well too often for me ...) the mouse passes a magic point in space and wooosh... scaling turns negative... You do not always see that this happens... Until you see the inside out effect in world...
Ok, i could tell you now, how to check for this effect INSIDE blender

... use textured mode and watch carefully ... You will see what i mean when you try it out. Or when we get our next basic tutorial ready ...
Now i hope THIS helped ? If not, then you should start reading the manuals

(and watching the tutorials
