Coordinate System in Cubemaps

i have some issues with Cubemaps which i don’t fully understand.

At first there is a simple Skybox, a large Cube that is texture mapped with OpenGL’s cubemapping capabilities. The 3D texturecoordinates are extracted from the cubes vertexcoordinates and interpolated between vertex- and fragmentshader.
The scene is rendering very well, but i think there is something wrong with the coordinate system.

The camera (view matrix) is located in the center and looking at (0,0,-1) corresponding to OpenGl’s right handed coordinate system. But at that position i’m looking at the image that is related to the cubemaps TextureCubeMapPositiveZ. I would expect to see the negative-z image because i’m looking at the negative z-axes.
X and Y are fine, positive-x at my right, negaitve-x at the left, positive-y at the top, negative-y at the bottom.

Is that orientation correct or is there anything wrong?

Related to this problem there is another one. In the center of the skybox i’m rendering a small sphere that’s using the cubemap for static reflections. At first i got some weird reflections that didn’t seem to be correct: The reflected parts of the cubemap were not (!) mirrored. With some random changes i finally found the right setting, i just inverted the z-coordinate in the fragmentshader and suddenly the reflection works as expected:

vFragColor *= texture(cubeMap, vec3(vVaryingCubeTexCoords.x, vVaryingCubeTexCoords.y, -vVaryingCubeTexCoords.z));

Again some issue with z-coordinate that’s irritating me but seems to be related to the first one.

Maybe someone is able to bring some enightment into this,

Cube map lookups are based upon texture coordinates. Which face you get depends entirely upon how you generate the texture coordinates. If the texture Z coordinate has the largest value and its value is positive, then you’ll get the positive-Z face.