[Algorithms] Per-Vertex interpolation of cubemap(cube with 6 different textures), through intersection of reflectionrays(3x)

[<mr_...@gm...>]

Hello,

(don't know, wether the [Algorithms] must be in subject field, if no, 
sorry for doublepost)
I have the following problem:
I have an 3d-object, witch is surrounded with a cube(boundingbox) on the 
different sites a textures of the envoirment, like cubemapping. But 
solong I understand, in OpenGL/Direct3D the procedery works on 
per-Pixel. Where the reflectionvectors where calculated and are 
interpolated(the vectors for self). But my problem is, that I don't want 
to use these per-pixel way, and go per-vertex(not with the actual ray, 
but with the texturecoordinates of ray-with-cube-intersections). Are 
there some reports or ideas how to archive this? Or this mathmaticaly 
impossible?

Thanks for any suggestions. And sorry for the bad english, hope it's 
still understandable.

Maxim