Question about face numbering in hexahedron cells

For the cell vtkTriQuadraticHexahedron, the face numbering is defined here as

The mid-surface nodes lies on the faces defined by (first edge nodes id’s, than mid-edge nodes id’s): (0,1,5,4;8,17,12,16), (1,2,6,5;9,18,13,17), (2,3,7,6,10,19,14,18), (3,0,4,7;11,16,15,19), (0,1,2,3;8,9,10,11), (4,5,6,7;12,13,14,15)

    * top
    *  7--14--6
    *  |      |
    * 15  25  13
    *  |      |
    *  4--12--5
    *
    *  middle
    * 19--23--18
    *  |      |
    * 20  26  21
    *  |      |
    * 16--22--17
    *
    * bottom
    *  3--10--2
    *  |      |
    * 11  24  9
    *  |      |
    *  0-- 8--1

I interpret this as follows:

front, right, back, left, bottom, top

But for higher order elements, explained in this pdf, the order in figure 8 seems to be

left,right,front,back,bottom,top.

I am guess that vtk use the same face order for all cells, so which one is wrong? or am I misinterpreting something?

Does anyone know if it is different face ordering for vtkTriQuadraticHexahedron and “higher order lagrange cells”, or if it is wrong in the documentation?