Tetrahedron with texture without scalars

I am trying to create a tetrahedron with a JPEG images on its faces.
I have thought of two approaches:

  1. Use the vtkPlatonicSolidSource and set the type to Tetrahedron. However, when I try to set my vtkTexture to the actor, the faces are colored according to the scalars that are assigned to the faces by default. The texture I supply seems to be ignored.
  2. Build my own vtkPolyData, and use SetTCoords on the point data. Hwoever, I am unsure which values to assign to each point, or even how many points to use.

I saw in vtkCubeSource that the cube is defined by 24 points and according texture coordinates. I’m a bit confused as to the usage of texture coordinate values -1.0 and -0.0. Should I use the same approach in defining my own tetrahedra?

If anyone could enlighten me with some pointer in the right direction, I would appreciate that very much…